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SOME   CONTRIBUTIONS   FROM   THE  LABORATORY  OF 
PHYSICS,  UNIVERSITY  OF  ILLINOIS 

TABLE  OF  CONTENTS 


Introduction 

Note   on    the    History   of   the    Department   of    Physics    at   the    University   of 
Illinois. 

A.  P.  Carman 

The  Design  of  a  Physical  Laboratory. — Reprinted  from  The  Brickbuilder,  Janu- 
ary, 1912. 

A.  P.  Carman 

A  Spontaneous  Electromotive  Force  in  Cells  of  Alkali  Metals. — Reprinted  from 
the  Physical  Review,  September,  1912. 

J.  W.  Woodrow 

Properties  of  the  Wehnelt  Cathode  Rays. — Reprinted  from  the  Transactions  of  the 
American  Institute  of  Electrical  Engineers,  October,  1912. 

C.  T.  Knipp 

lonization  of  Potassium  Vapor  by  Ultra-Violet  Light.— Reprinted  from  the  Phys- 
ical Review,  October,  1912. 

S.  H.  Anderson 

The  Magnetization  of  Heusler  Alloys  as  a  Function  of  the  Temperature  and  Cal- 
culation of  the  Intrinsic  Magnetic  Field. — Reprinted  from  the  Physical  Re- 
view, October,  1912. 

P.  W.  Gumaer 

A  Simple  Discharge  Tube  for  Demonstration  Purposes. — Reprinted  from  Science, 
December  13,  1912. 

C.  T.  Knipp 

Determination  of  Capacities  by  Means  of  Conjugate  Functions. — Reprinted  from 
Physical  Review,  December,  1912. 

J.  W.  Woodrow 

The  Projection  of  "The  Guinea  and  the  Feather"  Experiment.— Reprinted  from 
School  Science  and  Mathematics,  Vol.  13,  1913. 

A.  P.  Carman 

Some  Recent  Physical  Theory. — Reprinted  from  School  Science  and  Mathematics, 
Vol.  13,  1913. 

A.  P.  Carman 

Determination  Theorique  de  la  Variation  de  la  Masse  de  L'Electron  en  Fonction 
de  la  Vitesse. — Abstract  in  Archives  des  Sciences  physiques  et  naturelles, 
January,  1913. 

J.  Kunz 


2  UNIVERSITY    OF    ILLINOIS 

The  Velocity  of  Electrons  in  the  Photo-Electric  Effect,  as  a  Function  of  the  Wave 
Lengths  of  the  Light. — Reprinted  from  the  Physical  Review,  January,  1913. 

D.  W.  Cornelius 

lonization  of  Potassium  Vapor  by  Ultra-Violet  Light. — Reprinted  from  the  Phys- 
ical Review,  March,  1913. 

S.  H.  Anderson 

Rectifying  Properties  of  a  Photo-Electric  Cell. — Reprinted  from  the  Physical  Re- 
view, March,  1913. 

S.  H.  Anderson 

Air  Currents  and  Their  Relation  to  the  Acoustical  Properties  of  Auditoriums. — 
Reprinted  from  the  Engineering  Record,  March  8,  1913. 

F.  R.  Watson 

Conditions  .of  Sensibility  of  Photo-Electric  Cells  with  Alkali  Metals  and  Hydro- 
gen.—Reprinted  from  the  Physical  Review,  April,  1913. 

J.  G.  Kemp 

The  Use  of  Sounding-Boards  in  an  Auditorium. — Reprinted  from  The  Brick- 
builder,  June,  1913. 

F.  R.  Watson 

On  the  Beaded  Character  of  the  Cathode  Ray  Line  as  Revealed  by  Instantaneous 
Photographs  taken  at  Short  Range. — Reprinted  from  the  Physical  Review, 
July,  1913- 

C.  T.  Knipp 

On  the  Present  Theory  of  Magnetism  and  the  Periodic  System  of  Chemical  Ele- 
ments.— Abstract  from  "Original  Communications,"  Eighth  International  Con- 
gress of  Applied  Chemistry,  August,  1913. 

J.  Kunz 

The  Use  of  the  Photo-Electric  Cell  in  Stellar  Photometry. — Reprinted  from  the 
Astrophysical  Journal,  September,  1913. 

W.  F.  Schulz 

Thermal  and  Electrical  Conductivities  of  the  Alkali  Metals. — Reprinted  from  the 
Physical  Review,  September,  1913. 

J.  W.  Hornbeck 

A  Determination  of  e/m  and  v  by  the  Measurement  of  a  Helix  of  Wehnelt  Cathode 
Rays. — Reprinted  from  the  Physical  Review,  October,  1913. 

J.  B'.  Nathanson 

On  the  Use  of  Sealing  Wax  as  a  Source  of  Lime  for  the  Wehnelt  Cathode.— Re- 
printed from  the  American  Journal  of  Science,  December,  1913. 

Nellie  M.  Hornor 

Acoustical  Effect  of  Fi reproofed  Cotton-Flannel  Sound  Absorbers.— Reprinted 
from  Engineering  News,  January  29,  1914. 

F.  R.  Watson 

A  Determination  of  the  Sun's  Temperature.— Reprinted  from  the  Astrophysical 
Journal,  May,  1914. 

G.  A.  Shook 


DEPARTMENT  OF  PHYS'ICS 


THE    ELECTRICAL    MEASUREMENT    LABORATORY 

For  advanced   students    for   magnetic   and  electrical   work    for  high   precision. 
Calibration  standards  are  kept  connected  for  use  in  a  special  even  temperature  room. 


ONE  OF  THE  SMALL  LABORATORIES  FOR  SPECIAL   EXPERIMENTS  AND  RESEARCH 

These  laboratories  are  supplied  with  water,  gas,  compressed  air  and  experi- 
mental electrical  circuits,  and  double  shades  for  darkening.  There  are  twenty-five 
similar  laboratories, 


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DEPARTMENT  OF  PHYSICS 


NOTE  ON  THE  HISTORY  OF  THE  WORK  IN  PHYSICS 
AT  THE  UNIVERSITY  OF  ILLINOIS 

The  instruction  in  physics  at  the  University  of  Illinois  was  for  years 
connected  with  the  Mechanical  Engineering  Department.  Professor  S. 
W.  Robinson  who  was  the  Professor  of  Mechanical  Engineering  from 
1870  to  1878,  taught  physics  also.  From  various  pieces  of  apparatus 
which  he  devised  and  made,  remains  of  which  are  stiil  in  the  cabinets  of 
the  department,  we  know  that  there  was  a  spirit  of  investigation  even  at 
that  early  date.  Professor  Robinson  was  succeeded  by  Professor  S.  H. 
Peabody  who  taught  both  mechanical  engineering  and  physics  until 
elected  executive  head  of  the  University.  For  a  time  after  this  the 
instruction  seems  to  have  been  irregular,  at  one  time  being  connected 
with  the  department  of  Mining  Engineering.  In  1889  Samuel  W.  Strat- 
ton,  the  present  director  of  the  Bureau  of  Standards  at  Washington, 
was  made  Professor  of  Physics  and  reorganized  the  work  on  a  modern 
basis.  Professor  Stratton  was  a  graduate  of  the  University  in  mechani- 
cal engineering  and  had  also  been  instructor  in  the  architectural  and 
preparatory  departments.  He  brought  a  knowledge  of  practical  me- 
chanics and  pieces  of  apparatus  are  still  in  the  department  which  he 
made  for  the  work.  In  1892  Professor  Stratton  went  to  the  University 
of  Chicago  and  was  succeeded  by  Dr.  D.  W.  Shea.  Professor  Stratton 
started,  in  connection  with  the  Physics  Department,  courses  in  electrical 
engineering  and  purchased  imore  or  less  apparatus  for  this  work.  The 
University  began  to  get  larger  appropriations  from  the  State  for  main- 
tenance and  Professor  Shea  continued  the  development  of  the  electrical 
engineering  work  by  adding  much  apparatus  and  also  strengthening  the 
instructional  work  in  physics  by  more  equipment  adapted  to  the  newer 
laboratory  methods.  The  opening  of  Engineering  Hall  in  the  fall  of 
1894  removed  the  Department  of  Physics  from  the  limited  quarters  which 
it  had  occupied  in  University  Hall  for  many  years.  The  three  floors  of 
the  north  wing  of  the  Engineering  Hall  gave  to  the  department  a  floor 
space  of  about  eleven  thousand  square  feet  and  the  rooms  were  well 
equipped  for  the  instructional  side  of  the  work  in  physics.  The  dynamo 
laboratory  and  other  testing  rooms  for  the  electrical  engineering  work 
remained  in  the  basement  of  University  Hall  until  the  fall  of  1898 
when  the  present  Electrical  Engineering  Laboratory  was  completed  in 
connection  with  an  appropriation  for  the  new  heating  and  power  plant 
for  the  University.  In  December,  1895,  Professor  Shea  severed  his 
connection  with  the  University  to  become  the  first  professor  of  physics 
in  the  Catholic  University  of  America  at  Washington,  D.  C.  Albert  P. 


6  UNIVERSITY    OF    ILLINOIS 

Carman  was  elected  to  the  professorship  of  physics  and  began  his  services 
at  the  University  in  September  1896.  The  work  of  electrical  engi- 
neering was  not  separated  administratively  from  the  Department  of 
Physics  until  the  fall  of  1898.  This  separation  gave  better  opportunity 
for  developing  the  work  in  physics.  The  equipment  of  the  department 
was  within  the  next  few  years  practically  all  replaced  by  new  and  modern 
apparatus.  The  rapid  increase  in  the  number  of  engineering  students 
taking  required  courses  in  physics  made  it  necessary  not  only  to  replace 
the  old  equipment,  but  also  to  add  very  largely  to  the  equipment  and  also 
to  the  number  of  instructors  in  the  department.  This  expansion  ab- 
sorbed the  energy  of  the  department  for  a  number  of  years.  In  1904- 
1905  a  movement  was  started  to  obtain  a  new  and  modern  laboratory  for 
the  department.  The  legislature  of  Illinois  was  asked  in  1906  to  make 
an  appropriation  for  a  laboratory  but  other  interests  seemed  more  urgent. 
The  request  was  renewed  to  the  following  legislature  and  at  this  time  an 
appropriation  was  made  for  buying  the  present  site  for  a  new  building. 
In  the  following  legislature,  that  is,  in  1907,  an  appropriation  of  $250,000 
was  made  for  a  physics  building.  The  contract  for  this  building  was  let  in 
July  1908,  and  the  building  was  completed  and  dedicated  on  November 
27,  1909.  The  American  Physical  Society  made  this  the  occasion  for 
meeting  in  the  new  laboratory  for  the  Thanksgiving  meeting  of  that 
year.  The  program  of  the  dedication  shows  this  and  also  the  prominent 
part  that  the  address  and  lectures  of  Professor  A.  G.  Webster  had  at 
this  dedication. 

While  the  new  laboratory  with  its  excellent  facilities  and  equip- 
ment stimulated  the  research  work  of  the  department,  yet  this  work  had 
already  shown  increasing  activity  by  the  publications  of  several  years; 
and  indeed  the  demands  of  physical  research  were  in  no  small  part  re- 
sponsible for  the  new  building.  Below  is  given  a  list  of  publications  by 
members  of  the  department,  beginning  with  1909  to  the  close  of  1913: 

"On  the  Rate  of  Formation  of  Carbon  Monoxide  in  Gas  Producers,"  by  J.  K. 
Clement,  University  of  Illinois  Engineering  Experiment  Station,  Bulletin  No.  30, 
1909. 

"The  Time  Rate  of  Gas  Reactions  of  CO2,"  by  J.  K.  Clement,  University  of 
Illinois  Engineering  Experiment  Station  Bulletin  No.  30. 

"A  Simple  Cloud  Apparatus,"  by  C.  T.  Knipp,  Science,  December,  1909. 

"A  Substitute  for  Lampblack,"  by  F.  R.  Watson,  School  Science  and  Mathe- 
matics, Vol.  9,  1909. 

"Architectural  Acoustics,"  by  F.  R.  Watson,  Technograph,  Vol.  23,   1909. 

"The  Effect  of  a  Magnetic  Field  upon  the  Absorption  Spectra  of  Certain 
Rare  Earths,"  by  W.  F.  Schulz,  Astrophysical  Journal,  December,  1909. 

"On  the  Electron  Theory  of  Thermal  Radiation  for  Small  Values  of  (N  T)," 
by  J.  Kunz,  Physical  Review,  May,  1909. 

"On  the  Photoelectric  Properties  of  Sodium  Potassium  Alloy,"  by  J.  Kunz, 
Physical  Review,  August,  1909. 

"On  the  Photoelectric  Effect  of  Sodium  Potassium  Alloy  and  its  Bearing  on 
the  Structure  of  the  Ether,"  by  J.  Kunz,  Physical  Review,  September,  1909. 


DEPARTMENT  OF  PHYSICS  7 

"The  Thermal  Conductivity  of  Fire-Clay  at  High  Temperatures,"  by  J.  K. 
Clement  and  W.  L.  Egy,  University  of  Illinois  Engineering  Experiment  Station, 
Bulletin  No.  36,  1909. 

"The  Effect  of  Pressure  on  the  Electrolytic  Rectifier,"  by  A.  P.  Carman  and 
G.  J.  Balzer,  Physical  Review,  February,  1910. 

"The  Effect  of  Pressure  on  the  Aluminum  Rectifier,"  by  A.  P.  Carman  and 
G.  J.  Balzer,  Physical  Review,  June,  1910. 

"The  Instruction  of  Large  University  Classes,"  by  A.  P.  Carman  and  F.  R. 
Watson,  Science,  December,  1910. 

"A  Convenient  Form  of  Quartz  Tube  Mercury  Lamp,"  by  C.  T.  Knipp, 
Physical  Review,  May,  1910. 

"Temperature  and  Potential-Pressure  Relations  in  the  Mercury  Arc,"  by  C.  T. 
Knipp,  Physical  Review,  August,  1910. 

"An  Apparatus  for  Measuring  Sound,"  by  F.  R.  Watson,  Physical  Review, 
January,  1910. 

"Effect  of  Surface  Tension  upon  a  Falling  Jet  of  Water,"  by  F.  R.  Watson, 
Physical  Review,  February,  1910. 

"A  Peculiar  Heat  Phenomenon,"  by  F.  R.  Watson,  Science,  Vol.  XXXII. 

"Manual  of  Experiments  in  General  Physics  for  Engineering  Students,"  by 
W.  F.  Schultz,  Flanigan-Pearson  Co.,  Champaign,  Illinois,  June,  1910. 

"The  Absolute  Values  of  the  Moments  of  the  Elementary  Magnets  of  Iron, 
Nickel  and  Magnetite,"  by  Jakob  Kunz,  Physical  Review,  March,  1910. 

"On  the  Electromagnetic  Emission  Theory  of  Light,"  by  J.  Kunz,  American 
Journal  of  Science,  November,  1910. 

"On  the  Initial  Velocity  of  Electrons  as  a  Function  of  the  Wavelength  in  the 
Photoelectric  Effect,"  by  J.  Kunz,  Physical  Review,  November,  1910. 

"Magnetic  Properties  of  Heusler  Alloys,"  by  E.  B.  Stephenson,  Physical  Re- 
view, September,  1910. 

"The  Nature  of  Spark  Discharge  at  Very  Small  Distances,"  by  E.  H.  Wil- 
liams, Physical  Review,  September,  1910. 

"Comparison  of  the  Magnetic  Properties  of  Nickel  and  Iron,"  by  E.  H.  Wil- 
liams, Electrical  Review  and  Western  Electrician.  December  3,  1910. 

"Magnetic  Properties  of  Heusler  Alloys,"  by  E.  B.  Stephenson,  Illinois  Engi- 
neering Experiment  Station,  Bulletin  No.  47,  1910. 

"The  Design  of  a  Physical  Laboratory,"  by  A.  P.  Carman,  The  Brickbuilder, 
December,  1911. 

"Rays  of  Positive  Electricity  from  the  Wehnelt  Cathode,"  by  C.  T.  Knipp, 
Philosophical  Magazine,  December,  1911. 

"On  the  Positive  Potential  of  Metals  in  the  Photoelectric  Effect  and  the 
Determination  of  the  Wave-Length  Equivalent  of  Roentgen  Rays,"  by  J.  Kunz, 
Physical  Review,  September,  1911. 

"Echoes  in  an  Auditorium,"  by  F.  R.  Watson,  Physical  Review,  February,  1911. 

"Musical  Echoes,"  by  F.  R.  Watson,  Science,  October  6,  1911. 

"Laboratory  Physics,"  by  T.  S.  Taylor,  Manual  of  225  pages  for  Sophomore 
first  year  laboratory  work,  Gazette,  Champaign,  Illinois,  1911. 

"On  the  lonization  of  Various  Gases  by  the  Alpha  Particles  from  Polonium," 
by  T.  S.  Taylor,  Philosophical  Magazine,  April,  1911. 

"Some  Tests  on  Certain  Electrical  Insulators  at  High  Temperatures,"  by  W. 
W.  Stiffler,  Physical  Review,  April,  1911. 


8  UNIVERSITY    OF    ILLINOIS 

"The  Magnetization  of  Cobalt  as  a  Function  of  the  Temperature  and  the 
Determination  of  its  Intrinsic  Magnetic  Field,"  by  W.  W.  Stiffler,  Physical  Re- 
view, October,  1911. 

"Increase  of  Magnetic  Induction  in  Nickel  Bars  Due  to  Transverse  Joints," 
by  E.  H.  Williams,  Physical  Review,  July,  1911. 

"Spark  Discharge  at  Very  Small  Distances,"  by  E.  H.  Williams,  Physical  Re- 
view, June,  1911. 

"Effect  of  Frequency  on  the  Capacity  of  a  Condenser,  with  Kerosene  for  the 
Dielectric,"  by  S.  H.  Anderson,  Physical  Review,  January,  1912. 

"lonization  and  Photoelectric  Properties  of  Vapors  of  Alkali  Metals,"  by  S.  H. 
Anderson,  Physical  Review,  October,  1912. 

"Magnetism  and  Electricity,"  by  A.  P.  Carman,  Part  of  a  Text-Book  of 
Physics,  edited  by  A.  W.  Duff,  Philadelphia,  1912. 

"The  Magnetization  of  Heusler  Alloys  as  a  Function  of  the  Temperature  and 
Calculation  of  the  Intrinsic  Magnetic  Field,"  by  P.  W.  Gumaer,  Physical  Review, 
October,  1912. 

"Uber  Photoelectrische  Indicatoren  fur  electromagnetische  Wellen,"  (with  J. 
Kunz),  by  J.  G.  Kemp,  Jahrbuch  der  drahtlosen  Telegraphic  und  Telephonic,  1912. 

"On  the  Production  of  a  Helix  of  Rays  from  the  Wehnelt  Cathode,"  by  C.  T. 
Knipp,  Physical  Review,  January,  1912. 

"Rays  of  Positive  Electricity  from  the  Wehnelt  Cathode,"  by  C.  T.  Knipp, 
Physical  Review,  March,  1912. 

"Properties  of  the  Wehnelt  Cathode  Rays,"  by  C.  T.  Knipp,  Transactions  of 
American  Institute  of  Electrical  Engineers,  October,  1912. 

"A  Simple  Discharge  Tube  for  Demonstration  Purposes,"  by  C.  T.  Knipp, 
Science,  December  13,  1912. 

"On  the  Present  Theory  of  Magnetism  and  the  Periodic  System  of  Chemical 
Elements,"  by  J.  Kunz,  8th  International  Congress  of  Applied  Chemistry,  Volume 
XXII. 

"Radiation  Pyrometry,"  by  G.  A.  Shook,  Metallurgical  and  Chemical  Engi- 
neering, April  i,  1912. 

"Rechnungsapparat  fur  die  Bestimmung  von  thermodynamischen  Tempera- 
turen,"  by  G.  A.  Shook,  Physikalische  Zeitschrift,  August,  1912. 

"The  Number  of  Ions  Produced  by  an  Alpha  Particle,"  by  T.  S.  Taylor, 
Philosophical  Magazine,  April,  1912. 

"The  Electron  Theory  of  Magnetism,"  by  E.  H.  Williams,  University  of 
Illinois  Engineering  Experiment  Station,  Bulletin  No.  62,  1912. 

"A  Spontaneous  Electromotive  Force  in  Cells  of  Alkali  Metals,"  by  J.  W. 
Woodrow,  Physical  Review,  September,  1912. 

"Determination  of  Capacities  by  Means  of  Conjugate  Functions,"  by  J.  W. 
Woodrow,  Physical  Review,  December,  1912. 

"Rectifying  Properties  of  a  Photoelectric  Cell,"  by  S.  H.  Anderson,  Physical 
Review,  March,  1913. 

"lonization  of  Potassium  Vapor  by  Ultra-Violet  Light,"  by  S.  H.  Anderson, 
Physical  Review,  March,  1913. 

"Recent  Physical  Theory,"  by  A.   P.  Carman,    School   Science,  January,   1913. 

"The  Velocity  of  Electrons  in  the  Photo-electric  Effect  as  a  Function  of  the 
Wave  Lengths  of  the  Light,"  by  D.  W.  Cornelius,  Physical  Review,  January,  1913. 

"A  Substitute  for  a  Bronson  Resistance,"  by  J.  G.  Kemp  and  D.  W.  Cornelius, 
Physical  Review,  January,  1913. 


DEPARTMENT  OF  PHYSICS  9 

"Conditions  of  Sensibility  of  Photo-electric  Cells  with  Alkali  Metals  and  Hy- 
drogen," by  J.  G.  Kemp,  Physical  Review,  April,  1913. 

"On  the  Beaded  Character  of  the  Deflected  Cathode  Ray  Line  as  Revealed  by 
Instantaneous  Photographs  Taken  at  Short  Range,"  by  C.  T.  Knipp,  Physical  Re- 
view, April,  1913. 

"Determination  theoretique  de  la  variation  de  la  masse  de  1'electron  en  fonction 
de  la  vitesse,"  by  J.  Kunz,  Archives  des  Sciences  Physique  et  Naturelles,  1913. 

"Contributions  a  la  theorie  du  magnetisme,"  Journal  de  physique,  1913. 

"Effect  of  Gas  Currents  on  Sound,"  by  F.  R.  Watson,  Physical  Review,  Jan- 
uary, 1913. 

"The  Use  of  Sounding  Boards  in  an  Auditorium,"  by  F.  R.  Watson,  Physical 
Review,  March,  1913. 

"Air  Currents  and  the  Acoustics  of  Auditoriums,"  by  F.  R.  Watson,  Engineer- 
ing Record,  March  8,  1913. 


10 


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12  UNIVERSITY    OF    ILLINOIS 


THE  DESIGN  OF  A  PHYSICAL  LABORATORY 

(Reprinted  from  The  Brickbuilder,  January,    1912) 

ALBERT   P.    CARMAN. 

The  design  of  a  highly  specialized  building  like  a  university  physical 
laboratory  presents  many  problems  outside  the  experience  of  the  general 
architect.  The  literature  on  the  design  of  such  buildings  is  very  meager. 
A  number  of  laboratories  have  been  described  in  a  general  way,  but  often 
with  particular  emphasis  on  fittings  and  apparatus  and  with  little,  if  any, 
-discussion  of  the  problems  supposed  to  be  solved  in  the  design.  The 
following  article,  it  is  hoped,  will  help  fill  this  deficiency.  The  writer 
had  the  responsibility  of  making  specifications  for  the  design  of  a  physical 
laboratory  for  the  University  of  Illinois,  and  was  in  consultation  with 
architects  and  superintendents  during  the  erection  and  equipping  of  the 
building.  It  is  believed  that  an  explanation  of  the  plans  finally  used  will 
aid  those  who  have  to  design  this  type  of  building. 

About  twenty  leading  physical  laboratories  in  this-  country  were 
visited,  and  the  floor  plans  of  practically  all  of. the  recent  laboratories 
secured.  Several  months  were  spent  in  making  floor  plans  after  various 
schemes.  In  this  preliminary  work  an  architectural  student  was  em- 
ployed to  make  drawings  to  exact  scale.  The  possibilities  and  advantages 
of  various  schemes  were  thus  made  manifest,  and  the  essential  principles 
to  be  followed  in  the  design  became  evident.  In  these  preliminary  studies 
as  well  as  later,  Prof.  J.  M.  White  of  the  Department  of  Architecture 
and  Prof.  C.  T.  Knipp  of  the  Department  of  Physics  were  active  workers. 
This  preliminary  work  was  done  before  the  election  of  the  architect,  there 
being  a  delay  of  several  months  in  his  election,  and  the  result  was  that  a 
very  complete  and  definite  list  of  conditions  was  furnished  him.  The 
architect  (Mr.  W.  C.  Zimmerman  of  Chicago),  found  the  general  results 
of  these  preliminary  studies  very  helpful,  and  nowhere  asked  for  a  sacri- 
fice of  technical  requirements  to  get  architectural  effects. 

The  character  of  the  work  in  physics,  which  consists  of  the  usual 
undergraduate  courses,  and  of  a  considerable  and  growing  amount  of 
graduate  work  and  of  investigation,  fixed  the  number  and  general  char- 
acter of  the  rooms  desired.  The  site  was  also  fixed,  a  rectangular  space 
of  about  250  feet  square  with  a  south  front  for  the  building.  Fortunately 
or  unfortunately,  the  University  has  adopted  no  style  of  architecture,  so 
there  was  no  question  of  adapting  ecclesiastical  windows  or  projecting 
buttresses  of  classical  columns  to  the  requirements  of  unrestricted  light. 
Such  architectural  styles  present  very  difficult  problems  in  laboratory 
design.  They  have  been  solved  more  or  less  successfully,  but  the  difH- 


DEPARTMENT  OF  PHYSICS  13 

culty  is  such  that  we  cannot  wonder  that  more  than  one  professor  has 
suggested  that  the  best  style  for  a  laboratory  would  be  that  of  the  com- 
mon workshop,  and  perhaps  with  saw-tooth  roof  construction.  But 
efficiency  is  not  in  conflict  with  dignified  architecture,  and  a  university 
physical  laboratory  should  be  an  attractive  building  to  conform  to  the 
importance  of  the  science  in  university  work.  The  exterior  of  a  physical 
laboratory  is  important  to  the  man  of  physics,  principally  in  its  allowing 
a  convenient  window  spacing,  with  unobstructed  light,  as  well  as  being 
inexpensive,  so  that  no  interior  convenience  need  be  sacrificed.  The  style 
chosen  as  appropriate  to  our  surroundings  fitted  our  requirements  and 
money,  and  gave  us  a  dignified  and  pleasing  exterior  without  sacrificing 
interior  plans.  The  elevation  and  the  floor  plans  discussed  below  are 
shown  in  the  accompanying  illustrations. 

Freedom  from  mechanical  disturbances  is  of  such  obvious  impor- 
tance for  much  of  the  work  in  physics  that  it  received  early  consideration. 
Since  the  laboratory  is  for  university  instruction  the  location  is  neces- 
sarily central,  and  that  means  in  the  midst  of  various  activities  which 
may  cause  vibration.  The  first  thing  decided  was  to  use  extra  heavy 
masonry  walls  and  as  far  as  possible  to  carry  the  floors  on  masonry  walls 
rather  than  on  steel  columns.  This  involves  many  cross  walls  which  run 
the  full  length  of  the  building  and  give  a  rigid  cellular  design  as  seen  in 
the  floor  plans.  Over  three  million  bricks  were  used,  probably  twenty- 
five  per  cent  more  than  would  be  used  with  steel  columns  in  a  building 
of  this  size. 

Next  came  the  effect  of  room  arrangement  and  of  equipment  on 
stability.  To  avoid  the  disturbances  caused  by  the  movement  of  large 
classes  of  vigorous  students  the  large  laboratories  and  the  class  rooms 
are  put  on  the  west  side  of  the  building.  Most  of  the  students  naturally 
use  the  west  entrance,  so  that  this  design  minimizes  the  travel  across 
the  building.  The  east  side  of  the  building  is  thus  given  over  to  the 
twenty-five  smaller  laboratories  which  are  used  by  advanced  students 
and  individual  investigators  for  the  more  delicate  experiments.  This 
side  of  the  building  is  much  heavier  in  construction  owing  to  numbers 
of  interior  masonry  walls. 

An  equally  important  question  was  the  location  of  moving  machines. 
The  ventilating  fans,  the  liquid  air  plant  and  department  machine  shop 
are  placed  in  an  annex  building  which  has  a  foundation  separate  from 
that  of  the  main  building.  A  hydraulic  plunger  elevator  was  installed 
partly  on  account  of  its  simplicity  and  safety,  but  mainly  because  it  in- 
troduced no  rotating  machinery.  All  the  rotating  machinery  in  the  main 
building  is  concentrated  in  the  students'  workshop  at  the  northeast  cor- 
ner. The  floor  of  this  room  is  a  thick  block  of  reinforced  concrete 
floated  on  18  inches  of  sand  and  is  independent  of  the  walls  and  founda- 
tions. On  this  are  mounted  several  machine  tools  with  shafting  and 
motor  for  the  use  of  instructors  and  advanced  students.  This  method 
of  isolating  machinery  has  been  used  in  several  laboratories  and  found 


14  UNIVERSITY    OF    ILLINOIS 

satisfactory.  It  would  of  course  be  easy  to  restrict  work  in  this  shop 
at  times  if  any  particular  experimental  work  was  disturbed,  but  our  ex- 
perience indicates  that  this  will  rarely  occur.  As  heat  and  electric  power 
come  from  the  University  power  plant  we  have  had  no  problem  with 
boilers  and  prime-motors. 

An  equally  important  question  was  the  use  of  the  basement.  Many 
professors  regard  the  basement  as  the  choicest  room  on  account  of  its 
stability.  That  it  is  not  necessary  to  go  to  the  basement  for  stability  is 
shown  by  the  two  fine  research  laboratories  in  Washington,  the  Geo- 
physical Laboratory  and  the  Laboratory  of  the  Bureau  of  Standards. 
These  laboratories  do  not  depend  upon  the  basement  for  delicate  ex- 
perimental work.  The  objections  to  basement  rooms  are  that  they  are 
not  cheerful  and  that  they  are  liable  to  be  damp  at  certain  seasons  of 
the  year.  In  the  level  prairie  country  with  the  black  soil  of  the  "corn 
belt,"  basement  rooms  are  certainly  not  desirable  where  long  hours  must 
be  spent  in  experimental  work.  While  we  have  a  large  basement  ce- 
mented throughout,  part  of  it  is  cut  by  the  ventilating  ducts  and  the 
piping,  and  part  is  used  for  even-temperature  rooms,  a  large  battery 
room,  and  storage  room,  much  needed  in  working  laboratories.  All 
the  first  floor  laboratories  and  the  lecture  room  desks  have  independent 
masonry  piers  for  experiments.  The  wall  brackets  have,  however,  been 
found  equally  stable.  Even  on  the  upper  floors  the  wall  brackets  have 
been  satisfactory  for  all  general  purposes  and  are  particularly  good  near 
the  intersections  with  the  cross  walls. 

There  are  occasionally  demands  of  stability  made  by  physical  ex- 
periments which  test  to  the  limit  the  standard  masonry  pier.  To  meet 
this  exceptional  but  important  demand  three  special  piers  were  con- 
structed. A  heavy  block  of  concrete  was  built  on  a  thick  bed  of  loose 
gravel.  By  using  oil  cloth  over  the  gravel  the  concrete  formed  without 
becoming  part  of  the  gravel,  and  was  thus  "floated"  on  the  gravel.  The 
pier  was  then  erected  in  this  floating  foundation.  The  loose  gravel  trans- 
mits few  if  any  vibrations  and  the  inertia  of  the  heavy  concrete  founda- 
tion and  pier  is  an  additional  protection  against  vibrations.  A  pier  of 
this  kind  will  stand  the  test  of  a  free  mercury  surface. 

While  stability  is  demanded  in  a  physical  laboratory,  the  question 
of  convenient  arrangements,  service  rooms  and  "circulation"  or  ready 
access  is  none  the  less  important  in  a  laboratory  as  large  as  this  one. 
The  first  question  in  arrangement  was  the  location  of  the  large  experi- 
mental lecture  room.  A  lecture  room  requires  higher  ceilings  than  the 
ordinary  room  on  account  of  the  raised  seats  and  its  size.  It  must  be 
convenient  to  a  preparation  room  and  the  apparatus  cabinets,  and  should 
be  easily  accessible  to  the  auditors.  To  obtain  the  higher  ceiling  without 
breaking  floor  levels  the  lecture  room  is  often  put  on  the  top  floor.  This 
would  have  involved  in  our  case  a  climb  of  two  or  perhaps  three  flights 
of  stairs  which  was  undesirable  for  several  reasons.  The  problem  was 


DEPARTMENT  OF  PHYSICS  15 

finally  solved  by  using  the  court  between  the  wings  for  two  lecture 
rooms  and  a  preparation  room.  The  access  is  easy  and  the  location  re- 
duces the  disturbance  of  the  coming  and  going  to  a  minimum.  The 
lighting  is  by  skylights  with  a  north  exposure  and  no  side-lights ;  allow- 
ing the  room  to  be  quickly  and  completely  darkened  by  horizontal  screens 
rolling  on  tracks  between  the  skylights  and  the  glass  ceiling.  The  size 
of  the  lecture  room  forms  a  question  on  which  there  is  evidently  .much 
difference  of  opinion.  After  a  thorough  test  it  was  decided  that  50  feet 
should  be  the  maximum  distance  of  any  seat  from  the  lecture  desk  for 
an  experimental  lecture.  Using  a  standard  opera  chair  with  folding 
tablet  arm  there  are  265  seats  within  this  radius,  which  number  is  ample 
since,  for  teaching  efficiency,  a  lecture  section  of  over  200  is  undesirable. 
The  second  lecture  room  seats  120  and  shares  the  preparation  room  with 
the  large  lecture  room.  An  apparently  minor  point  that  caused  much 
thought  in  the  lecture  room  design  was  the  position  of  the  entrance.  A 
rear  entrance  is  undesirable  because  it  is  not  in  full  view  of  the  lecturer 
and  so  encourages  tardiness.  The  entrance  should  be  placed  so  as  not 
to  interfere  with  the  passage  from  the  desk  to  the  preparation  room. 
In  a  physics  lecture  roo,m  it  is  desirable  to  have  a  diagonal  curtain  across 
one  front  corner  so  that  a  lantern  can  be  operated  for  projecting  ex- 
periments. These  requirements  are  met  very  satisfactorily  in  the  larger 
lecture  room  and  fairly  so  in  the  smaller  lecture  rooms.  There  is  a 
scheme  used  in  some  foreign  laboratories  of  having  the  entrance  to  the 
preparation  room  and  cabinets  directly  back  of  the  lecture  desk,  with 
sliding  blackboards  and  a  projection  curtain  coming  down  over  this 
entrance.  It  seems,  however,  better  to  keep  the  needed  blackboard,  and 
curtain  independent  of  an  entrance. 

The  location  and  arrangement  of  the  apparatus  cabinets  is  a  special 
feature  of  the  design.  These  are  placed  in  the  north  central  part  of  the 
building  and  extend  through  three  stories.  The  principle  of  the  library 
stack  is  used,  a  mezzanine  floor  being  introduced  on  each  story.  This 
scheme  practically  doubles  the  available  apparatus  room.  These  stacks 
are  accessible  from  each  corridor  by  a  special  stairway  and  by  an  eleva- 
tor. The  elevator  shaft  runs  from  the  unpacking  room  in  the  base,ment 
to  the  fourth  floor  and  has  openings  to  the  main  corridor  on  each  floor, 
and  also  to  each  of  the  six  floors  with  apparatus  stacks.  By  using  large 
rubber-tired  trucks  which  can  be  run  on  the  elevator  it  is  easy  to  transfer 
heavy  apparatus  to  any  part  of  the  building.  The  central  location  of 
these  apparatus  stacks  makes  them  convenient  to  all  the  working  rooms 
of  the  building.  Indeed  the  preparation  rooms  for  the  lecture  rooms  and 
for  the  large  laboratories  on  the  second  and  third  floors  open  directly 
into  these  stacks.  In  addition  to  these  central  cases  each  small  labora- 
tory is  fitted  with  a  case  for  the  apparatus  and  supplies  which  are  in 
current  use  in  that  room. 

For  each  large  laboratory  there  is  a  preparation  room  supplied  with 
facilities  for  adjusting  apparatus  and  making  minor  repairs,  and  also  an 


l6  UNIVERSITY    OF    ILLINOIS 

administration  office  with  assistants'  desks  where  reports  are  corrected 
and  records  kept.  On  each  floor  there  is  a  chemical  room  and  one  or 
more  photographic  rooms.  Interior  dark  rooms  are  also  found  in  several 
of  the  smaller  laboratories.  Some  of  these  laboratories  are  fitted  with 
double  curtains  held  in  place  by  deep  side  slots  so  that  the  room  can  be 
easily  darkened  for  ordinary  purposes.  The  device  of  using  double 
curtains  bound  together  but  mounted  on  separate  spring  rollers  fixed 
vertically  over  each  other  is  due  to  Prof.  D.  C.  Miller.  It  is  inexpensive 
and  satisfactory. 

The  class  rooms,  seminary  room,  offices,  coat  rooms,  etc.,  involve 
no  questions  peculiar  to  laboratory  design.  The  experimental  electric 
circuits  and  switchboards,  and  the  distribution  of  gas,  water,  and  com- 
pressed air  are  important  features  in  a  modern  laboratory,  but  they  are 
perhaps  more  in  the  nature  of  equipment  rather  than  subjects  of  design. 
For  the  extension  of  this  wiring  and  piping  either  temporary  or  perma- 
nent accessible  shafts  are  provided  in  all  parts  of  the  building.  This 
provision  cannot  be  neglected  in  a  fire-proof  building. 

The  fourth  floor  is  also  completely  finished.  It  contains  extensive 
photographic  rooms  with  a  large  north  skylight  and  rooms  which  are 
available  for  various  experiments  in  light,  sound,  and  electric  waves. 
There  are  no  special  points  of  design  involved  in  the  planning  of  this 
floor. 

In  addition  to  the  question  of  general  design  in  the  planning  of  a 
laboratory  there  arise  many  questions  in  the  design  of  the  individual 
rooms  and  in  their  fittings,  but  these  questions  of  detail  are  beyond  the 
purpose  of  this  paper. 


DEPARTMENT  OF  PHYSICS 


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[Reprinted  from  the  PHYSICAL  REVIEW,  Vol.  XXXV.,  No.  3,  Sept.,  1912.)  ' 


A   SPONTANEOUS    ELECTROMOTIVE-FORCE    IN    CELLS    OF 

ALKALI    METALS. 

BY  JAY  W.  WOODROW. 

IN  working  with  photo-electric  cells,  it  was  found  that  when  the  cell 
was  insulated  in  the  dark  the  alkali  metal  would  develop  a  negative 
charge.     As  all  attempts  to  remove  this  effect  were  unsuccessful,  it  was 
decided  to  investigate  the  phenomena  more  carefully.     The  results  of 
these  experiments  will  be  described  in  the  following  paper. 

The  apparatus  was  set  up  as  shown  in  Fig.  I.     The  alkali  metal  was 
placed  in  the  cell  C  and  as  high  a  vacuum  as  possible  obtained  by  means 
of  a  Gaede  pump  so  that  a  per- 
fectly pure  surface  could  be  pro- 
cured.    The  different  metals  in- 
vestigated   were    caesium, potas- 
sium,  and    an   alloy  of   sodium 
and  potassium  formed  by  melt- 
ing together  masses  of  the  two 
proportional    to   their   atomic 
weights  respectively.     Through- 
out the  investigation,  the  cell  was  kept  carefully  screened  from  the  light 
by  the  box  D. 

In  measuring  the  potential,  the  electrode  of  the  alkali  metal  which  was 
connected  to  one  pair  of  quadrants  of  the  electrometer  Q  was  insulated 
by  raising  the  plunger  of  the  key  K.  The  other  electrode  and  the  other 
pair  of  quadrants  were  earthed.  The  maximum  potential  was  deter- 
mined from  the  deflection  of  the  electrometer  which  had  a  sensitiveness 
of  1 60  mm.  per  volt. 

In  order  to  measure  the  current  which  the  cell  would  give,  the  interior 
of  a  small  cylindrical  condenser  (capacity  =  24.55  E.S.U.)  was  connected 
in  as  shown  at  H.  The  outer  cylinder  of  the  condenser  was  connected  to 
a  potentiometer  by  means  of  which  any  desired  potential  could  be 
obtained.  After  raising  the  plunger  of  the  key  K,  the  potential  on  the 
exterior  of  the  condenser  was  gradually  increased  so  as  to  keep  the 
electrometer  always  at  the  zero  position.  From  the  known  potential 
and  capacity,  the  charge  drawn  into  the  condenser  in  a  given  time  was 
determined  and  from  this  the  current  was  readily  calculated. 


2O4 


JAY  W.  WOODROW. 


[VOL.  XXXV. 


MEASUREMENT  OF  THE  POTENTIAL. 

The  plunger  of  the  key  K  was  raised  and  the  electrometer  readings 
were  taken  at  regular  intervals.  At  first  the  deflection  increased  rapidly, 
but  after  a  few  hours  the  reading  became  constant.  The  curve  obtained 
by  plotting  potential  against  time  resembles  a  saturation  curve.  Typical 
cases  are  shown  in  Fig.  2.  Curve  I.  was  obtained  with  a  cell  in  which 
the  electrodes  consisted  of  an  aluminium  wire  placed  parallel  to  the 
surface  of  the  alloy  of  sodium  and  potassium.  The  cell  from  which 
Curve  II.  was  obtained  contained  caesium  and  platinum  electrodes.  The 
time  required  for  the  cells  to  attain  the  maximum  potential  was  found 
to  depend  upon  the  size  and  distance  between  the  electrodes.  In  one 
cell  in  which  the  earthed  electrode  was  simply  the  end  of  a  platinum  wire, 
it  required  over  thirty  hours  to  attain  the  maximum  potential ;  while  the 

other  cells  in  which  larger  elec- 
trodes were  used  i  cached  the  maxi- 
mum value  in  from  two  to  four 
hours.  If  instead  of  earthing  the 
aluminium  (or  platinum)  electrode, 
it  was  kept  at  a  constant  positive 
potential  equal  in  value  to  the  neg- 
ative potential  attained  by  the 
alkali  metal,  the  deflection  was  re- 
duced to  zero. 

Five  different  cells  with  the  sodium-potassium  alloy  for  the  alkali 
electrode  were  investigated  and  the  mean  maximum  negative  potentials 
in  volts  are  given  in  Table  I.  Cell  III.  was  constructed  with  two  elec- 

TABLE  I. 


f  1  ^a- 

1                 2 

54567 

Fig.  2. 

Number  of 
Cell. 

Maximum  Potential  Attained. 

Remarks. 

Charcoal  at 

25°  C. 

Charcoal  in 
Liq.  Air. 

No  Charcoal 
Tube. 

I. 

2.2 

1.5 

Al  electrode  earthed. 

II. 

2.0 

Al  electrode  earthed. 

1.5 

Al  electrode  earthed. 

III. 

1.5 

Pt  electrode  earthed. 

2.4 

Al  electrode  earthed. 

IV. 

2.5 

Tube  filled  with  hydrogen. 

2.8 

After  electric  discharge. 

1.6 

Al  electrode  earthed. 

V. 

2.4 

After  electric  discharge. 

Caesium 

2.6 

Potassium 

2.0 

trodes,  in  addition  to  the  platinum  electrode  which  was  in  contact  with 
the  allov,  so  that  measuiements  could  be  taken  with  either  an  aluminium 


No.  3.]  SPONTANEOUS  ELECTROMOTIVE-FORCE.  2O5 

or  platinum  electrode  earthed  while  at  the  same  time  no  change  would 
be  made  in  the  connections  between  the  alloy  and  the  electrometer. 
It  will  be  seen  that  the  maximum  potential  obtained  in  the  two  cases 
was  identical.  If  the  effect  had  been  due  to  a  contact  potential  difference 
between  the  alloy  and  the  platinum  or  aluminium,1  the  magnitude  of 
the  potential  in  the  two  cases  would  have  differed  as  the  contact  difference 
of  potential  between  potassium  and  aluminium  is  1.9  volts  while  that 
between  potassium  and  platinum  is  4.1  volts.2  Cells  exactly  similar  to 
the  above  in  construction,  containing  clean  mercury  in  a  high  vacuum, 
showed  no  leak  which  could  be  measured  when  treated  as  were  the  cells 
of  alkali  metals.  It  is  also  worthy  of  notice  that  the  mean  maximum 
potential  obtained  with  Cell  I.  when  the  charcoal  tube  was  immersed  in 
liquid  air  is  exactly  equal  to  that  obtained  with  Cell  III.  to  which  no 
charcoal  tube  was  attached. 

Interesting  phenomena  were  shown  by  Cell  IV.  This  cell  contained 
strips  of  palladium  which  had  been  made  to  absorb  great  quantities  of 
pure  hydrogen  by  using  it  as  the  cathode  in  an  electrolytic  cell  of  dilute 
sulphuric  acid.  Upon  heating  the  palladium  the  tube  was  filled  with 
hydrogen,  but  very  little  change  was  observed  in  the  maximum  potential. 
However,  upon  passing  an  electric  discharge  from  an  induction  coil 
through  the  cell  for  several  minutes,  the  potential  was  increased  quite 
perceptibly.  This  increase  of  the  potential  would  disappear  in  a  few 
days  but  could  be  renewed  by  means  of  another  discharge.  This  effect 
of  the  electric  discharge  was  even  more  pronounced  in  another  cell, 
No.  V.,  which  contained  no  hydrogen.  It  was  rather  surprising  to  find 
that  although  the  hydrogen  was  shown  to  exert  considerable  pressure 
within  the  tube,  yet  it  seemed  to  make  no  change  or  at  least  very  little 
change  in  this  effect. 

EFFECT  OF  TEMPERATURE  UPON  THE  MAXIMUM  POTENTIAL. 
The  effect  of  the  temperature  upon  this  potential  was  next  investigated. 
The  cell  was  heated  by  means  of  an  electric  furnace  in  which  the  wires 
were  so  wound  as  not  to  produce  a  magnetic  field.  The  temperatures 
were  read  on  a  good  mercury-in-glass  thermometer  suspended  so  that  the 
bulb  was  in  contact  writh  the  glass  walls  of  the  cell.  This  of  course  gave 
only  a  close  approximation  to  the  actual  temperature  of  the  alkali  metal 
but  was  thought  to  be  sufficiently  accurate  for  the  purpose  of  the  experi- 
ment. The  temperatures  below  room  temperature  were  obtained  by 
partially  immersing  the  cell  in  ice  and  a  mixture  of  salt  and  ice  which  was 

1  Cf.  Jakob  Kunz,  PHYS.  REV.,  XXXI.,  p.  538,  1910.     Cf.  F.  K.  Richtmyer,  PHYS.  REV., 
XXIX.,  p.  74,  1909. 

2  Winkelmann,  Handbuch  der  Physik,  Vol.  4,  p.  855. 


206 


JAY  W.  WOOD  ROW. 


[VOL.  XXXV. 


contained  in  an  earthed  tin  vessel.  A  set  of  values  is  given  in  Table  II. 
for  the  mean  potentials  observed  with  one  cell.  The  potentials  are 
recorded  in  volts. 

TABLE  II. 

Potential  as  a  Function  of  the  Temperature. 


Temperature. 

Maximum  Potential. 

Temperature. 

Maximum  Potential. 

-15°C. 

2.00 

60°  C. 

2.18 

0°C. 

1.92 

65°  C. 

2.24 

15°  C. 

1.20 

75°  C. 

2.21 

25°  C. 

0.73 

80°  C. 

2.20 

30°  C. 

0.91 

105°  C. 

2.13 

40°  C. 

1.59 

120°  C. 

2.02 

50°  C. 

1.91 

160°  C. 

2.00 

Fig.  3. 


The  curves  in  Fig.  3  both  indicate 
that  the  minimum  effect  is  obtained 
at  about  25°  C.  and  the  maximum 
at  about  75°  C.;  while  above  the  lat- 
ter the  potential  decreases  slightly 
and  then  remains  very  nearly  con- 
stant with  further  increase  in  the  tem- 
perature. At  the  higher  temperatures 
the  maximum  potential  was  reached 


in  a  few  minutes  after  insulation.     This  fact  led  to  an  investigation  of 
the  current  which  the  cell  would  give. 

EFFECT  OF  TEMPERATURE  UPON  THE  CURRENT. 

The  current  was  measured  as  explained  earlier  in  the  paper,  and  the 
desired  temperatures  were  obtained  as  in  the  previous  case  where  the 
potential  was  determined.  In  Fig.  4  are  shown  curves  which  represent 
the  current  given  by  two  different  sodium-potassium  cells.  These  curves 
are  seen  to  be  identical  with  those  which  Richardson1  obtained  for  the 
current  b  itween  a  hot  platinum  wire  and  a  metal  cylinder  surrounding 
it  in  a  high  vacuum.  That  is,  for  temperatures  above  30°  C.,  the  current 
given  by  a  cell  with  electrodes  of  platinum  and  an  alloy  of  sodium  and 
potassium  in  a  high  vacuum  will  when  carefully  screened  from  light  be 
represented  by 


The 


where  a  and  b  are  constants  and  T  is  the  absolute  temperature, 
following  constants  were  calculated  for  Cell  No.  VI., 

*O.  W.  Richardson,  Proc.  Camb.  Phil.  Soc.,  XI.,  p.  286,  1902. 


No.  3.) 


SPON TA  NEO US  ELECT ROMO TI VE-FORCE. 


207 


a  =  0.18,     b  =  11,000; 
and  for  Cell  VII., 

a  =  o.oi,     b  =  10,000. 

The  dotted  curve  in  Fig.  4  is  the  curve  obtained  by  using  the  former 
of  the  two  sets  of  constants  in  the  above  theoretical  equation.  The 
close  agreement  between  these  curves  and  the  theoretical  curves  indicates 
that  the  current  is  due  to  an  emission  of  positive  particles  from  the 
surface  of  the  alkali  metals.  Dr.  S.  H.  Anderson,  working  in  this  labora- 


Ct  HTIGR  \DC 


iOO          13.0       /40 


-40       -SO 


Fig.  4. 


Fig.  5. 


tory,  has  shown  in  a  paper  which  will  appear  later  that  the  same  curves 
are  obtained  from  the  alkali  metals  caesium  and  potassium. 

However,  at  the  temperatures  below  room  temperature  the  above 
equation  does  not  hold.  A  maximum  value  was  obtained  at  about  o°  C. 
as  is  shown  by  the  curves  in  Fig.  5.  As  the  temperature  was  still  further 
decreased  the  magnitude  of  the  current  decreased  and  at  the  temperature 
of  liquid  air  it  was  too  small  to  be  measured  with  any  degree  of  accuracy. 
It  will  be  seen  that  the  curves  in  Fig.  5  are  the  same  as  those  in  Fig.  4 
drawn  on  a  different  scale  so  as  to  show  the  small  maximum  at  o°  C. 
It  was  observed  that  even  with  the  best  vacuum  possible,  the  suiface 
of  the  sodium-potassium  alloy  would  not  remain  pure  if  an  aluminium 
electrode  were  used.  After  a  few  weeks  a  white  film  would  appear  which 
caused  a  decrease  in  the  maximum  potential  and  current  obtained  from 
the  cell.  Upon  examining  several  cells  it  was  noticed  that  only  those 
which  had  been  left  short-circuited  for  some  time  in  the  dark  showed 
this  effect.  If  care  were  taken  not  to  leave  the  cell  in  the  dark  while 
short-circuited,  the  surface  would  remain  pure  for  a  long  time.  In  the 
later  cells  investigated  the  aluminium  electrode  was  replaced  by  one  of 


2C>8  JAY  W.  WOODROW.  [VoL.  XXXV. 

platinum.  After  four  months  these  cells  still  show  a  perfectly  pure 
alkali-metal  surface.  That  is,  a  small  beam  of  light  is  so  reflected  from 
the  metal  that  one  cannot  see  the  spot  where  it  strikes  the  surface. 
Time  has  not  permitted  a  further  investigation  to  determine  whether 
this  formation  of  a  film  was  due  to  the  gases  contained  in  the  aluminium 
electrode  or  to  some  action  betwreen  the  alkali  vapor  and  this  electrode. 

No  attempt  has  been  made  to  explain  all  the  phenomena  described 
here.  However,  all  the  results  point  to  the  conclusion  that  some  sort  of 
positively  charged  particles  are  given  off  by  the  alkali  metals  in  a  high 
vacuum.  As  Dr.  Anderson  in  a  paper  which  is  to  appear  later  has  shown 
that  at  the  high  temperatures  this  emission  of  positive  electricity  is  so 
great  as  to  counterbalance  the. ordinary  photo-electric  effect  in  the  light, 
we  conclude  that  this  action  is  taking  place  in  the  light  as  well  as  when 
screened  from  light  but  is  overbalanced  by  the  emission  of  negatively 
charged  electrons  at  ordinary  temperatures  in  the  latter  case. 

If  we  consider  the  current  given  by  these  cells  as  due  to  positive  par- 
ticles emitted  from  the  surface  of  the  metal,  the  number  leaving  the 
surface  can  be  computed.  For  we  have  that 


. 

n  =  7  „  xx 20  =  X-3X 


where  n  is  the  number  leaving  the  surface  per  second,  i  is  the  current, 
and  e  is  the  charge  on  each  carrier.  At  a  temperature  of  25°  C.  the 
current  was  found  to  be 

i  =  1.9  X  io-16  E.M.U. 

Taking  e  to  be  1.5  X  io~20,  this  gives  for  the  number  leaving  the  surface 
per  second, 

X  IP"15 
1.5  X  io- 

It  is  interesting  to  compare  this  with  the  total  number  of  atoms  in  the 
surface  layer  of  the  alkali  metal.  An  approximate  value  of  the  average 
area  of  cross-section  of  the  atom  in  the  alloy  used  is  1.7  X  io~15  sq.  cm. 
The  area  of  the  surface  was  8.4  sq.  cm.  so  that  the  total  number  in  the 
surface  layer  was 

•   •          •        rdHo^  -  s  x  I0'6-    - 

Hence,  the  ratio  of  the  total  number  of  atoms  in  the  surface  layer  to  the 
number  of  particles  leaving  this  surface  per  second  is 


1.3  X  io5 


No.  3.J  SPONTANEOUS  ELECTROMOTIVE-FORCE.  2CX) 

That  is,  if  the  current  is  considered  as  due  to  positive  particles  shot  out 
from  the  metal,  only  one  atom  out  of  3.8  X  io10  of  those  on  the  surface 
layer  would  be  required  to  emit  a  positive  particle  per  second  in  order 
to  account  for  the  total  current.  At  120°  C.  the  current  was  2.6  X  io~13 
E.M.U.,  and  consequently, 

n  =  1.7  X  io7. 

The  ratio  of  the  total  number  of  atoms  in  the  surface  layer  of  positive 
particles  emitted  per  second  would  be 

5  X  io15 

ITlotf =  3  x  I0 ' 

These  results  seem  to  indicate  that  only  a  very  small  proportion  of  the 
atoms  are  active  and  that  the  number  increases  with  the  temperature. 
If  it  can  be  proved  that  this  current  is  due  to  positive  particles  shot  off 
from  the  active  atoms  (or  molecules),  it  will  give  a  direct  proof  of  the 
theory  of  radiation  which  assumes  that  only  a  small  proportion  of  the 
molecules  of  a  radiating  body  are  active. 

These  investigations  are  to  be  continued  further  in  order  to  investigate 
more  thoroughly  the  nature  of  this  positive  emission  and  to  determine 
the  source  of  the  energy.  The  present  investigation  has  been  carried 
out  during  the  past  year  under  the  direction  of  Dr.  Kunz,  whom  the 
author  wishes  to  thank  most  heartily  for  his  many  helpful  suggestions 
and  for  his  never-failing  interest  and  aid  in  the  progress  of  the  work. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 

URB ANA- CHAMPAIGN,  ILLINOIS 


A  paper  presented  at  the  Urbana  Section  meeting 
of  the  American  Institute  of  Electrical  Engineers, 
Urbana,  111.,  Feb.  21,  1912. 

Copyright  1912.     By  A.  I.  E.  E. 
(Subject   to  final   revision,  for   the   Transactions'). 


PROPERTIES    OF    THE    WEHNELT    CATHODE    RAYS 


BY  C.  T.  KNIPP 


The  discharge  of  electricity  through  gases  is  a  subject  that 
has  had  a  most  wonderful  growth, — a  growth  possibly  greater 
than  that  of  any  other  single  division  in  physics.  With  the 
discovery  of  cathode  rays,  X-rays,  radio-activity,  and  rays  of 
positive  electricity,  a  new  era  was  begun.  The  cathode  rays 
were  the  first  of  the  above  to  be  brought  to  our  attention,  how- 
ever, but  little  was  known  of  their  properties  until  the  researches 
of  the  last  decade.  About  fifteen  years  ago  the  wonderful 
X-  or  Roentgen  rays  were  discovered.  A  few  years  later  came 
that  almost  revolutionizing  discovery  of  radio-activity, — revo- 
lutionizing because  we  are  obliged  to  change  our  conceptions 
regarding  the  molecule  and  atom.  Another  of  equal  importance 
because  of  its  bearing  upon  chemical  composition,  is  afforded 
by  J.  J.  Thomson's  recent  investigations  on  rays  of  positive 
electricity. 

These  avenues  in  physical  science  that  have  been  opened  by 
the  researches  of  such  eminent  physicists  as  Crookes,  Roentgen, 
Thomson,  Rutherford,  the  Curies,  Webnelt  and  others,  have 
played,  and  will  play  a  most  important  part  on  the  problems  of 
the  consititution  of  matter  and  the  nature  of  electricity.  It  is 
safe  to  say  that  we  know  more  nearly  what  is  going  on  when  elec- 
tricity passes  through  a  gas  than  when  it  passes  through  either 
liquids  or  solids. 

Let  us  take,  for  instance,  an  ordinary  discharge  tube  (exhibiting 
tube)  connected  to  a  quick  acting  pump  (e.g.,  the  Gaede). 
First  notice  the  form  of  the  tube  and  its  construction.  This  one 
is  1.5  meters  long,  and  about  four  cm.  in  diameter.  The  two 
electrodes  are  flat  disks  of  aluminum  about  two  cm.  in  diameter 

1883 


•<?   £ 


1884  KNIPP:   WEHNELT  CATHODE  RAYS  [Feb.  21 

and  placed  one  at  either  end.     The  connection  to  the  pump 
is  at  the  center. 

In  operating  this  tube  it  is  necessary,  as  stated  above,  to 
have  some  means  of  exhausting  it.  This  may  be  done  by  any 
one  of  a  number  of  pumps  that  are  on  the  market.  A  time 
honored  method  is  to  use  a  Geissler  mercury  pump.  To  cause 
a  current  to  flow  through  the  tube  a  suitable  source  of  high  po- 
tential must  be  available,  such  as  an  electrostatic  machine  or 
an  induction  coil.  We  have  here  an  induction  coil  (exhibiting 
coil)  that  will  give  a  spark  of  10  or  15  cm.  The  ease  with  which 
the  current  passes  through  the  tube  depends  upon  the  amount  of 
air  in  the  tube,  i.e.,  upon  the  pressure.  When  the  pressure  is 
76  cm.  of  mercury  (atmospheric)  the  discharge  passes  with  great 
difficulty,  requiring  several  thousand  volts  per  centimeter,  but 
as  the  pressure  is  reduced  by  pumping,  the  current  passes  more 
readily,  and  soon  a  stage  is  reached  where  the  resistance  offered 
by  the  gas  in  the  tube  is  a  minimum.  In  order  to  study  the 
discharge  critically  it  must  take  place  in  but  one  direction — 
it  must  be  unidirectional.  The  current  from  the  induction  coil 
may  readily  be  made  so  by  introducing  a  gap  in  the  circuit. 
The  current  may  be  reversed  by  a  commutator.  Notice  that 
no  discharge  takes  place  on  closing  the  circuit  of  the  induction  coil 
when  the  pressure  is  atmospheric.  We  will  now  start  the  pump. 
Its  action  is  rapid  and  in  a  few  moments  the  pressure  will  be 
reduced  sufficiently  to  allow  the  discharge  to  pass.  Notice 
how  stringy  it  is.  By  means  of  the  parallel  spark  gap  at  the 
induction  coil,  we  see  that  this  1.5  meters  of  tube  corresponds  to 
about  3  cm.  of  air  at  atmospheric  pressure.  Notice  that  it  is 
becoming  more  fuzzy — that  it  is  spreading  out  and  filling  the 
tube.  On  reversing  the  direction,  we  notice  but  little  difference 
between  the  ends.  Note  the  color.  Also  note  that  the  parallel 
gap  must  now  be  very  much  reduced  to"  cause  it  to  spark 
there.  The  tube  now  is  completely  filled  with  the  discharge, 
and  this  is  the  stage  where  the  resistance  offered  by  the  remaining 
gas  is  a  minimum.  The  parallel  gap  now  must  be  very  short 
to  allow  a  spark  to  pass  there.  This  stage  is  known  as  the 
Geissler  tube  stage,  and  the  pressure  is  1/300  or  1/400  of  the 
original  pressure  in  the  tube,  (i.e.,  two  or  three  mm.  of  mercury). 
We  notice  now  a  marked  difference  in  the  appearance  of  the  two 
ends  of  our  discharge  tube.  On  reversing  the  current  the  il- 
lumination at  the  ends  interchanges.  Obviously  then,  since 
our  current  is  unidirectional,  the  effect  within  the  tube  where 


1912]  KNIPP:  WEHNELT  CATHODE  RAYS  1885 

the  current  enters  is  different  from  that  where  it  leaves.  The 
electrode  where  it  enters  is  called  the  anode,  while  that  where 
the  current  leaves  is  the  cathode.  If  we  are  to  examine  our 
current  as  to  its  direction,  we  would  find  that  the  luminous  end 
is  the  anode  and  the  other  the  cathode.  On  close  examination 
we  see  that  the  cathode  is  covered  with  a  velvety  glow.  Just 
beyond  is  a  dark  space  known  as  Crooke's  dark  space.  Im- 
mediately beyond  this  is  a  luminous  part  called  the  negative 
glow,  while  beyond  is  another  dark  space  called  Faraday's  dark 
space.  The  luminous  region  extending  from  this  to  the  anode 
is  called  the  positive  column.  Notice  the  alternate  dark  and 
bright  spaces  in  this  column.  They  are  called  striae.  At  first 
they  were  close  together  and  barely  visible,  but  as  the  exhaustion 
is  pushed  they  separate  and  now  are  more  prominent.  Their 
position  and  prominence  depend  on  a  variety  of  conditions  such 
as  pressure,  size  of  tube,  gas  in  the  tube,  etc. 

As  the  pressure  is  reduced  the  positive  column  recedes  towards 
the  anode.  The  spark  is  now  passing  with  more  difficulty  as  may 
be  shown  by  the  parallel  spark  gap. 

We  now  notice  a  new  phenomenon  within  our  discharge  tube. 
The  tube  is  beginning  to  glow  with  a  faint  greenish  phosphores- 
cent light  which  is  rapidly  becoming  more  and  more  marked. 
The  color  of  this  light  depends  on  the  kind  of  glass  used — soda 
glass  producing  a  greenish  and  lead  glass  a  bluish  phosphores- 
'cence.  This  phosphorescence  is  due  to  minute  particles  shot 
off  normally  from  the  surface  of  the  cathode  and  impinging  on 
the  surface  of  the  glass.  These  particles  travel  in  straight  lines 
and  have  a  high  velocity. 

They  have  many  interesting  properties.  They  carry  negative 
charges  of  electricity,  are  deflected  by  either  a  magnetic  or  an 
electrostatic  field,  have  a  mass  which  is  roughly  1/1000  that  of 
the  hydrogen  atom,  may  ionize  a  gas  through  which  they  pass, 
i.e.,  by  reason  of  their  high  velocity  they  may  break  up  by  col- 
lision the  molecules  of  a  gas  into  component  positive  and  negative 
charges,  and  lastly  these  particles  possessing  large  kinetic  energy 
and  high  velocity  are  the  origin  of,  or  better,  the  direct  cause  c.. 
the  production  of  the  X-  or  Roentgen  rays  with  which  we  are 
now  so  familiar. 

The  fact  that  these  rays  travel  in  straight  lines  enables  us 
by  suitable  diaphragms  to  isolate  the  cathode  beam.  A  tube 
thus  constructed  is  called  a  Braun  tube.  Sometimes  the  tube 
is  constructed  with  two  parallel  plates  mounted  on  the  inside 


1886  KNIPP:   WEHNELT  CATHODE  RAYS  [Feb.  21 

for  electrostatic  deflection,  while  the  magnetic  deflection  is  pro- 
duced by  bringing  the  poles  of  an  electromagnet  in  position  from 
the  outisde.  The  Braun  tube  at  once  suggests  possibilities  of 
hysteresis  measurements,  and  this  has  been  successfully  done  by 
Professor  Ryan  in  the  Ryan-Braun  tube. 

We  will  now  pass  to  the  work  on  cathode  rays  by  Professor 
Wehnelt  of  Berlin.  In  1904  he  found  that  the  stream  of  catho- 
dic  particles  could  be  very  much  intensified  if  an  incandescent 
salt  is  used  for  the  cathode.  In  fact  he  found  that  he  could 
dispense  with  the  induction  coil  or  Wimshurst  machine  and  con- 
nect directly  to  a  storage  battery  of  comparative  low  voltage. 
The  ease  with  which  these  ions  escape  from  the  hot  lime  surface 
makes  it  possible  for  the  discharge  to  pass,  provided  the  condi- 
tions of  temperature  of  lime,  pressure  in  tube,  etc.,  are  right, 
at  an  impressed  potential  difference  of  less  than  100  volts. 

This  cathode  which  bears  his  name  is  constructed  as  follows: 
A  narrow  strip  of  platinum  foil,  about  1.5  mm.  wide,  is  mounted 
between  the  ends  of  the  two 
leading-in  wires.  On  the  cen- 
ter of  this  strip  is  placed  a 
minute  quantity  of,  say  cal-  °l 
cium  chloride,  or  indeed  a 
touch  of  high  grade  sealing 
wax  will  answer  seemingly 
equally  well.  FlG-  l 

In  operating,  the  platinum  strip  is  gradually  heated  to  in- 
candescence, while  the  positive  terminal  of  our  storage  battery 
is  put  in  contact  with  the  anode  and  the  negative  terminal  to  the 
hot  lime.  When  the  conditions  within  the  tube  are  right  a 
sharply  outlined  beam  will  issue  normally  from  the  surface  of 
the  hot  lime  and  travel  the  full  length  of  the  tube,  provided, 
as  stated  above,  the  pressure  is  low  enough.  In  case  the  pressure 
is  too  high  the  beam  will  be  diffused  and  absorbed  by  the  re- 
maining gas  in  the  tube. 

For  certain  purposes  this  beam  of  Wehnelt  cathodic  rays  has 
distinct  advantages  over  the  ordinary  cathode  beam.  The  ions 
are  moving  slower  and  hence  are  more  readily  deflected  by  either 
a  magnetic  or  an  electrostatic  field ;  the  beam  starts  directly  from 
the  source  without  the  use  of  diaphragms  and  hence  the  lime 
cathode  may  be  placed  directly  in  the  fields;  and  lastly,  the 
discharge  is  very  steady  since  the  current  is  continuous  and  not 
intermittent  as  in  the  induction  coil.  In  other  respects  these 
rays  are  the  same  as  the  ordinary  cathode  rays. 


1912]  KNIPP:   WEHNELT  CATHODE  RAYS  1887 

Let  us  now  turn  to  the  electrostatic  and  magnetic  deflection 
of  these  rays. 

First,  consider  the  theory  of  the  electric  deflection.  Let 
OX,  Fig.  1,  be  the  path  of  the  undeflected  beam.  M  N  the 
electric  field  plates,  and  A  B  the  screen.  Let  Y  =  the  electric 
force,  d  =  the  length  of  the  field  plates,  /  =  the  distance  of  the 
screen  from  the  source  and  y  the  displacement  to  be  determined. 

The  equation  of  motion  is 


where  m  is  the  mass  of  the  electron,  and  e  the  charge  of  electricity 

on  it. 

Hence 

A       1          d'y          YC 
Accel.  =     ,  ;;    =  -    -  =  a 
d  t2          m 

The  deflection  downward  at  mn  is, 


and  the  velocity  downward, 


Ye       _      Ye    d 
t  —  — 


m  m     v 


Now  the  additional  deflection  downward  in  going  from  m  to  the 
screen  A  B  is, 


_ 


m     v        v 
Hence  whole  distance  downward  is, 


. 


m 

Ye  . 

mv2  - 

J±j 

mv2  * 
which    may    be    written 


,£       Yed  (l-d\ 
v2         m    v   \     v     ) 


A.e 


1888  KNIPP:   WEHNELT  CA  THODE  RA  YS  [Feb.  21 

where  A  is  a  constant  depending  upon  the  electr6static  field  and 
the  geometrical  data  of  the  discharge  tube.  We  see  that  the 
electric  deflection  is  inversely  proportional  to  the  energy  of 
the  particle,  i.e.,  inversely  proportional  to  mvz.  This  is  always 
true. 

We  will  now  turn  to  the  magnetic  deflection.  We  will  place 
the  electromagnet  so  that  its  lines  are  coterminous  with  the  elec- 
trostatic lines.  Then  from  our  knowledge  of  .the  behavior  of  a 
moving  charge  in  a  magnetic  field  the  deflection  will  be  at  right 
angles  to  the  plane  of  the  board — i.e.,  at  right  angles  to  the  elec- 
trostatic deflection.  The  case  is  similar  to  the  electrostatic 
one,  and  in  order  to  get  the  z  displacement  it  is  only,  necessary 

to  substitute  for the  value  -  — ,  where  H  is   the  magnetic 

m  m 

force,  and  e,  v  and  m  are  the  same  as  before. 
Making  this  substitution  we  get, 


_  *•.,(,_  4) 

mv      \          2  / 


If  the  magnetic  field  is  not  coterminous  with  the  electric  field, 
then  we  must  prime  d  and  /,  thus, 


m  v  2 

In  either  case  we  may  write, 

Be 

=  ^T  (2) 

where  B  is  a  constant  depending  upon  the  magnetic  field  strength 
and  the  geometrical  data  of  the  discharge  tube.  Again  notice 
that  the  magnetic  deflection  is  inversely  proportional  to  the 
momentum,  i.e.,  inversely  proportional  to  mv. 

The  above  method  is  based  upon  the  supposition  that  the 
fields  (both  electric  and  magnetic)  end  abruptly  at  the  edge  of 
their  respective  plates.  This  as  we  well  know,  is  not  the  case. 
A  discussion  of  the  necessary  correction  in  the  electrostatic  case 
is  too  long  to  enter  upon  here.  Under  certain  conditions  the 
error  is  not  appreciable  —  those  conditions  are  that  /  be  large  in 
comparison  to  d,  and  also  to  the  distance  apart  of  the  electric 
field  plates. 

However  in  the  magnetic  case  it  is  appreciable  and  I  will  out- 
line a  method  recently  devised  by  Professor  ].  ].  Thomson  that 


1912] 


KNIPP:   WEHNELT  CATHODE  RAYS 


1889 


is  free  from  error.  Figure  2  is  looking  down  from  above  and 
along  the  lines  of  force.  Thomson  places  a  triangular  coil, 
of  length  /  and  width  at  base  d,  with  the  base  resting  on  the  screen 
A  B.  This  coil  is  wound  with  a  layer  of  very  fine  wire,  and  is 
connected  to  some  flux  measuring  instrument  such  as  a  Grassot 
flux  meter. 
The  formula  that  applies  is, 


II        Be 


mv   n  d        mv 


(2) 


where  /  is  the  total  flux  through  the  coil  as  indicated  by  the 
fluxmeter,  /  the  length  of  the  triangular  coil,  d  the  width  at  the 
base,  and  n  the  number  of  turns. 

We  thus  have  in  equations  (1)  and  (2)  the  electric  and  mag- 
netic deflections  respectively.     It  is  clear  that  if  we  apply  the 

two  fields  simultaneously  the 
spot  on  our  screen  will  not  be 
along  either  the  y  or  z  axis, 
but  at  some  intermediate 
position,  P.  Obviously  then 
we  can  calculate,  by  combin- 
ing equations  (1)  and  (2), 
FIG.  2  either  the  velocity  v  of  the 

electron,  or  the  ratio  of  the 

charge  on  the  electron  to  the  mass  of  the  same,  e/m.  Solving 
for  v  between  the  two  equations  we  have, 


v  = 


A  e 

mvy 


Be 

mz 


from    which 


and 


A    z 

-= 

By 


e 

m 


v  =    -=  --  =     i  — 


zv 

F 


(3) 
(4) 


where  y  is  the  electric  and  z  the  magnetic  displacements  respect- 
ively. 

We  have  before  us  the  apparatus  intended  to  show  these 
deflections.  The  electrostatic  plates  may  be  seen  within,  and 
by  their  position  the  electric  deflection  will  be  vertical,  as  will 
be  shown  by  the  spot  moving  vertically  when  the  electric  field 
is  turned  on.  Reversing  the  direction  of  the  field  reverses  the 
direction  of  the  deflection. 


1890  KNIPP:   WEHNELT  CATHODE  RAYS  [Feb.  21 

The  magnetic  field  is  furnished  by  this  vertical  two-part  sol- 
enoid. As  previously  stated  the  deflection  of  the  spot  due  to 
the  magnetic  field  will  be  at  right  angles  to  the  magnetic  lines 
of  force.  Turning  on  the  field  we  get  a  deflection  to  the  right, 
then  to  the  left  when  the  field  is  reversed. 

By  turning  on  the  two  fields  simultaneously,  we  get  a  resultant 
displacement,  say,  in  the  first  quadrant.  We  may  readily 
change  this  to  any  other  quadrant  by  the  proper  directions  of 
the  fields.  The  magnitude  of  the  deflections,  both  electric  and 
magnetic,  may  be  readily  adjusted  to  any  value. 

It  is  interesting  in  this  connection  to  give  the  results  of  a 
calculation  made  from  data  taken  with  this  apparatus.  The 
numerical  values  of  the  constants  are,  A  =  70  X  1010,  B  =  4.6 
X  102;  and  the  deflections  were  adjusted  to,  y  =  4.8  cm.,  z  = 
4.8  cm. 

From  which  v  =  1.6  X  109,  and  e/m  =  1.5  X  107. 
These  values  compare  very  favorably  with  the  values  obtained 
by  numerous  investigators  for  the  case  of  the  ordinary  cathode 
rays.     For  the  latter  we  have  v  =  2.6  X  109,   and  e/m  =  1.7 
X  107. 

This  experiment  suggests  several  possible  practical  applica- 
tions. The  system  is  sensitive  and  responds  readily  to  slight 
variations  in  the  respective  fields,  but  it  is  doubtful,  because  of 
the  difficulty  in  heating  the  lime  cathode,  whether  its  practica- 
bility will  ever  extend  beyond  the  research  laboratory. 

We  saw  in  equation  (2)  that  a  magnetic  field  deflects  the 
cathode  particle  at  right  angles  to  the  direction  of  the  field. 
The  question  naturally  arises,  what  will  be  the  path  of  the  ion 
if  the  magnetic  field  is  indefinitely  increased?  The  simplest 
case  is  when  the  field  is  at  right  angles  to  the  path  of  the  ions. 
The  velocity  of  the  ion  remains  constant.  It  has  been  shown  that 
the  normal  force  towards  the  center  =  H  e  v.  This  must  be 
equal  to  the  centrifugal  force  of  the  moving  ion  acting  outward 
along  the  radius  of  curvature.  This  from  dynamics,  is 

m  v2 
P 

where  p  is  the  radius  of  curvature. 

These  two  forces  must  be  equal,  hence, 

mtf 
Hev  =  - 


1912]  KNIPP:   WEHNELT  CATHODE  RAYS  1891 

m  v  ...         .     .    , 

or  p  =  -77 —  =  radius  or  circle. 

rl  e 

Suppose  that  our  magnetic  field 

H  =  50  gausses 
and  v  =  109  cm.-sec. 

also  e/m  =  1.7  X  107. 
Then 

mv  109                    100 

~JTe""  50X1.7X107   :    ~~85~ 

Hence  for  a  field  of  50  lines  per  square  centimeter  we  should 
expect  the  ion  to  travel  in  a  circle  of  approximately  2.5  cm. 
diameter. 

We  have  an  apparatus1  designed  especially  to  show  this  circular 
path.  Its  distinctive  feature  is  the  mounting  of  the  Wehnelt 
cathode.  (See  foot  note  for  reference  giving  full  description). 

In  operating  an  apparatus  like  this,  it  is  more  convenient  to 
change  the  order  of  manipulation;  that  is,  to  place  the  cathode 
so  that  the  cathode  beam  passes  parallel  to  the  axis  of  the  glass 
cylinder — parallel  to  the  magnetic  lines  of  force — and  later  turn 
the  cathode  until  the  emerging  beam  takes  up  a  position  at 
right  angles  to  the  lines  of  force.  If  the  vacuum  is  high  enough 
the  beam  should  reach  to  the  millemite  screen,  and  if  it  is  truly 
parallel  to  the  lines  of  force,  it  will  suffer  no  deviation.  The 
millemite  screen  lights  up.  Now  we  will  turn  on  the  magnetic 
field.  The  beam  is  but  little  affected.  Next  turn  the  cathode 
slightly.  Notice  the  form  that  the  beam  assumes — a  long  grace- 
ful spiral.  Further  turning  brings  the  spiral  into  greater  prom- 
inence— winds  it  up  as  it  were.  It  is  interesting  at  this  point 
to  note  the  effect  of  varying  the  magnetic  field.  Again  leaving 
the  magnetic  field  constant  let  us  vary  the  current  by  changing 
the  temperature  of  the  hot  platinum.  These  effects  are  very 
marked  and  are  in  full  accord  with  theory.  Turning  the  cathode 
still  farther  increases  the  pitch  of  the  helix  when  finally  it  de- 
grades (theoretically)  into  a  circle. 

An  ion,  then,  shot  at  random  across  a  magnetic  field,  will,  in 
obedience  to  the  forces  acting  upon  it,  move  in  a  spiral.  If 
the  field  is  uniform  the  path  described  is  a  helix.  The  tendency 
is  for  an  ion  to  move  along  the  lines  of  magnetic  force.  That 
this  is  the  case  was  seen  in  the  experiment  just  described.  Yet 

1.   C.  T.  Knipp,  Phys.  Rev.,  Vol.  34,  Jan.  1912. 


1892  KNIPP:   WEHNELT  CATHODE  RAYS  [Feb.  21 

a  further  experiment  is  necessary  to  thoroughly  convince  us  of 
this  statement. 

Fig.  3  shows  a  discharge  tube  of  unusual  form — circular  but 
not  reentrant.  The  magnetizing  field  coil,  in  the  form  of  atoroid 
so  as  to  secure  a  uniform  circular  field  within,  is  of  heavy  wire 
and  of  few  turns.  The  tube  is  thus  plainly  visible.  It  has 
affixed  to  it  one  of  the  specially  mounted  Wehnelt  cathodes. 

To  begin  with,  we  will  set  the  cathode  so  that  the  emerging 
beam  lies  in  the  plane  of  the  coil  when  no  field  is  on.  You  can 
plainly  see  the  beam  strike  the  glass  a  few  centimeters  above  the 
cathode.  In  this  position  it  is  tangential  to  the  axis  of  the  dis- 
charge .tube.  If  now,  as  we  saw  by  the  previous  experiment, 
the  ions  tend  to  follow  the  lines  of  force,  the  beam  should,  when 
a  strong  magnetic  field  is  turned  on,  follow  the  axis  of  the  dis- 
charge tube  in  the  form  of  a  spiral.  And  so  it  does.  In  fact, 
the  beam  as  far  as  we  can  judge  by  the  eye,  follows  the  axis 
exactly  as  is  shown  by  the  photograph  of  the  discharge  repro- 
duced in  Fig.  3.  This,  however,  is  not  in  accord  with  theory. 
The  form,  no  doubt,  is  a  spiral  of  long  pitch  and  very  short 
radius,  and  thus  its  form  as  such  is  not  detected  'by  the  eye.  It 
is  clearly  seen  to  be  a  spiral  when  weaker  magnetic  fields  are 
employed.  The  question  naturally  suggests  itself,  will  the  beam, 
(or  better,  the  resulting  spiral)  still  follow  the  axis  of  the  tube 
when  the  cathode  is  turned  through  an  angle?  On  turning  the 
cathode  we  find  that  in  this  case,  too,  the  axis  is  followed.  The 
inference  at  once  is  that  the  helix  as  a  whole  does  follow  the 
lines  of  magnetic  force,  while  the  ions  only  tend  to  follow  them. 

For  some  months  past  we  have  been  trying  to  realize  acorn- 
pact  yet  long  helical  beam  of  cathode  rays  for  purposes  of  elec- 
trical measurements,  believing  that  such  a  beam  under  proper 
conditions  would  form  a  very  sensitive  indicator.  The  sprial 
experiment  described  above  was  the  first  step  in  the  realization 
of  such  a  beam.  We  shall  present  now  the  beam  as  we  have 
perfected  it  to  date.  The  apparatus,  Fig.  4,  is  simple,  even  more 
so  than  those  that  were  just  used. 

It  consists  of  a  large  tube,  about  6  cm.  in  diameter,  and  about 
60  cm.  long.  One  end  is  closed  round,  while  the  other  is  cut 
off  square  and  closed  by  a  plate  of  heavy  glass  on  which  is  spread 
a  willemite  screen.  A  nipple  is  fused  in  near  the  round  end  and 
through  this  is  inserted  the  specially  mounted  Wehnelt  cathode 
— it  being  free  to  turn  at  right  angles  to  the  axis  of  the  discharge 
tube.  A  transparent  (loosely  wound)  solenoid  is  slipped  over 


PLATE  CXXVIII 

A.  I.  E.  E. 
VOL.  XXXI,  NO.  10 


[KNIFPJ 


FIG.  3 


[KNIPP] 


FIG.  4 


1912]  KNIPP:   WEHNELT  CATHODE  RAYS  1893 

the  tube.  This  solenoid  is  carried  a  few  turns  beyond  either 
end  in  order  to  secure  a  uniform  field  the  full  length  of  the  tube. 

We  will  begin  by  sending  the  discharge  along  the  axis  of  the 
tube.  The  beam  may  not  be  overly  sharp.  Turning  on  the 
magnetic  field  changes  its  position  but  little,  but  has  the  effect 
of  making  it  compact  and  thus  bringing  it  into  prominence  the 
full  length  of  the  discharge  tube.  The  beam,  however,  is  not 
uniform.  It  has  the  form  of  a  ribbon  twisted  several  complete 
turns,  the  latter  depending  upon  the  strength  of  the  magnetic 
field.  This  sharpening  of  the  beam  is  nicely  shown  on  the  wille- 
mite  screen.  On  turning  the  cathode,  the  beam  first  takes  the 
form  of  a  long  graceful  helix  (Fig.  4)  which  increases  in  pitch 
as  the  turning  is  continued.  The  winding  up  as  it  were  of  the 
helix  is  beautifully  shown  by  the  end  view  on  the  willemite 
screen.  On  close  examination  it  is  seen  that  the  cross  section 
of  the  helix  as  pictured  by  the  screen  is  very  clear  cut.  Turning 
our  attention  again  to  the  helix,  we  see  that  it  is  deflected  by  an 
outside  magnetic  field,  even  though  this  field  is  much  weaker 
than  that  within  the  solenoid.  With  the  other  conditions  re- 
maining constant  we  again  notice  the  effect  on  the  diameter  of 
the  helix  by  varying  the  potential  difference  impressed  on  the 
discharge  tube.  Again  as  before,  keeping  the  discharge  constant, 
we  note  the  effect  of  varying  the  temperature  of  the  Wehnelt 
cathode.  Lastly  if  we  swing  the  central  part  of  the  coil  back 
and  forth  the  helix  within  keeps  apparently  in  perfect  step,  i.e., 
compressing  the  solenoid  increases  the  magnetic  field,  which  in 
turn  increases  the  pitch  of  the  helix. 

Your  attention  was  called  a  moment  ago  to  the  realization  of 
a  long  helical  beam  and  to  the  statement  that  such  a  beam  under 
proper  conditions  forms  a  sensitive  indicator.  The  possible 
application  is  in  determining  the  nature  and  constitution  of  light. 
Professor  J.  J.  Thomson  has,  from  theoretical  considerations, 
come  to  the  conclusion  that  ordinary  light  may  not  necessarily 
consist  of  a  smooth  wave  motion  through  the  ether  but  that  it 
may  consist  of  pulses, — in  short,  may  consist  of  positively  and 
negatively  charged  ions.  It  seems  barely  possible  that  the  ques- 
tion may  be  tested  experimentally  by  some  such  helix  as  we 
have  been  studying.  The  theory  underlying  the  experiment  is 
that  if  a  beam  of  light  were  concentrated  on  a  helix  ne'ar  its 
source  the  picture  on  the  willemite  screen  would  show  blurred 
if  the  light  consists  of  positively  and  negatively  charged  ions, 
but  would  not  be  affected  if  light  is  an  undulatory  motion 


1894  KNIPP:   WEHNELT  CATHODE  RAYS  [Feb.  21 

through  the  ether.  Why  the  image  in  the  former  case  would 
be  blurred  is  not  difficult  to  explain.  The  cathode  beam  consists 
of  negatively  charged  ions.  If  these  are  hit  by  both  negatively 
and  positively  charged  ions  some  will  be  deflected  in  one  direc- 
tion and  others  in  another,  the  sum  total  effect  being  a  blurring 
of  the  image  on  the  screen. 

Whether  Professor  Thomson's  view  is  correct,  time  only  can 
tell;  nor  is  the  failure  of  an  experiment  like  the  one  described 
conclusive  evidence  against  the  theory,  for  it  will  require  refine- 
ments in  methods  and  manipulation  that  far  exceed  the  compara- 
tively crude  results  that  we  have  described  in  this  paper. 


(Reprinted  from  the  PHYSICAL  REVIEW,  Vol.  XXXV.,  No.  4.  Oct.;  1912.] 


IONIZATION   AND    PHOTO-ELECTRIC    PROPERTIES    OF 
VAPORS  OF  ALKALI   METALS. 

BY  S.  HERBERT  ANDERSON. 

INTRODUCTION. 

IT  is  a  well-recognized  fact  that  the  photo-electric  effect  may  give 
some  definite  information  of  the  nature  of  radiation  and  of  the 
distribution  of  energy  in  light  waves.  The  importance  of  this  phenom- 
enon makes  it  very  desirable  to  have  reliable  quantitative  data  of  the 
relation  between  the  wave-length  of  the  incident  light  illuminating  a 
metal  and  the  positive  potential  acquired  by  the  metal  under  such  condi- 
tions. So  far  the  results  of  different  observers  show  great  discrepancies. 
E.  Ladenburg,1  working  in  the  region  X  2,700  to  X  2,000,  obtained  data, 
which,  according  to  his  interpretations,  show  that  the  relation  is  a  linear 
one  and  a  verification  of  Plank's  theory  of  radiation  which  may  be  ex- 
pressed by 

*' 


where  P  is  the  potential,  e  the  elementary  electrical  charge,  k\  a  constant 
and  n  the  frequency  of  the  incident  light.  Hull,2  working  in  the  region 
X  1,710  to  X  1,230  obtained  data  which  he  interprets  in  the  same  way, 
while  Kunz,3  working  over  a  range  of  X  5,000  to  X  2,000  obtained  data 
which  verify  his  theory  of  radiation,4  which  may  be  expressed  by 


1  Phys.  Zeits.,  VIII.,  p.  590,  1907. 
»  Am.  Jr.  of  Sc.,  XXVIIL,  p.  251,  1909. 
»  PHYS.  REV.,  XXXIIL,  p.  208,  1911. 
4  PHYS.  REV.,  XXIX.,  p.  212,  1909. 


24O  5.   HERBERT  ANDERSON.  [VOL.  XXXV. 

That  is,  the  potential  which  the  illuminated  metal  acquires  varies  as  the 
square  of  the  frequency  and  not  simply  as  the  frequency.  More  recently 
Wright1  has  obtained  curves  for  the  relation  between  the  wave-length 
and  positive  potential  which  differ  both  from  the  results  of  Ladenburg 
and  Hull  and  of  Kunz,  and  might  indicate  that  the  phenomenon  is  of  a 
resonance  nature  which  would  be  in  accord  with  neither  Plank's  nor 
Kunz's  theory. 

Furthermore,  the  work  of  Millikan2  and  Wright  (/.  c.)  shows  that  the 
magnitude  of  the  photo-electric  effect  is  largely  determined  by  surface 
conditions.  Gehrts3  has  shown  that  the  reflection  of  electrons  and 
secondary  electrons  may  produce  effects  which  amount  to  40  or  50  per 
cent,  of  the  original  effects  ;  and  consequently  the  methods  of  investiga- 
tion must  be  such  as  to  avoid  these.  Hughes4  has  shown  that  metal 
surfaces  procured  by  distillation  of  the  metals  in  vacuo  give  a  larger  photo- 
electric potential  than  is  obtained  from  polished  surfaces  which  have 
not  been  treated  to  a  glow  discharge,  and  is  much  more  stable  and  con- 
stant. The  work  of  all  these  observers  shows  that  the  photo-electric 
effect  is  far  from  a  simple  one.  The  exact  law  cannot  be  known  until  all 
the  factors  entering  in  are  known  and  understood. 

In  the  physical  laboratory  of  the  University  of  'Illinois  considerable 
work  has  been  done  upon  the  photo-electric  effect  of  alkali  petals.  The 
advantages  of  work  with  these  metals  are:  (i)  a  clean  surface  can  easily 
be  obtained  by  distillation  in  vacuo,  and  (2)  these  metals  give  larger 
photo-electric  currents  than  any  other  metals.  In  investigations  carried 
on  by  Professor  Kunz,  Dr.  J.  G.  Kemp  and  the  author,  it  has  been 
observed  that  there  is  present  in  tubes  prepared  as  photo-electric  cells, 
containing  alkali  metals,  a  conduction  due  to  something  else  than  the 
electron  current  arising  from  the  photo-electric  action.  It  was  thought 
that  possibly  this  was  due  to  ionization  of  the  vapor  of  the  alkali  metals. 
Therefore  the  following  investigation  was  undertaken  to  determine  (i) 
whether  or  not  there  was  a  spontaneous  ionization  of  the  vapors  of  alkali 
metals  and  (2)  to  determine  the  magnitude  of  the  currents  of  conduction 
for  different  temperatures. 

Fuchtbauer8  has  made  some  investigation  of  the  spontaneous  ionization 
of  sodium  vapor  at  temperatures  ranging  from  190°  C.  to  330°  C.  In  a 
later  paper6  he  gives  some  results  obtained  with  caesium  vapor,  but  in 


1  PHYS.  REV.,  XXXIIL,  p.  43. 

2  PHYS.  REV.,  XXXIV.,  p.  68,  1912. 

3  Ann.  der  Phys.,  36,  p.  995,  1911. 

4  Proc.  Camb.  Phil.  Soc.,  XVI.,  p.  167. 
8  Phys.  Zeits.,  10,  p.  374,  1909. 
•Phys.  Zeits.,  12,  p.  225,  1911. 


No.  4.]  PROPERTIES   OF    VAPORS   OF^ALKALI  METALS.  241 

an  atmosphere  of  helium  of  196  mm.  pressure,  which  would  render  the 
results  quite  different  from  those  obtained  with  caesium  vapor  alone. 
The  temperatures  he  used  for  caesium  were  from  150°  C.  to  210°  C.  In 
the  former  paper  he  gives  a  curve  of  conduction  in  sodium  vapor  which 
has  very  little  of  the  characteristic  features  of  an  ionization  curve.  In 
the  latter  paper  curves  are  obtained  which  do  approximate  to  ionization 
curves. 

Fredenhagen1  in  an  investigation  on  the  electrons  given  off  from  sodium 
and  potassium  made  some  observations  of  the  conductivity  of  the  vapors 
of  these  metals.  He  heated  the  potassium  vapor  up  to  420°  and  the 
sodium  up  to  500°  and  found  no  currents  that  were  measurable  with  a 
galvanometer  that  gave  a  deflection  of  one  millimeter  for  a  current  of 
3.7  X  icr10  amperes.  The  tube  used  for  this  part  of  his  work  was  of 
the  same  type  used  by  the  author  (Fig.  I,  A). 

The  investigations  of  Fiichtbauer  and  Fredenhagen  do  not  throw  much 
light  on  the  photo-electric  phenomenon.  One  cannot  tell  whether  the 
conductivity  they  obtained  is  due  to  the  vapor  alone  or  to  particles 
given  off  from  the  metal  which  was  present  in  the  tube  containing  the 
electrodes.  And  it  is  especially  desirable  to  know  whether  or  not  there 
is  a  spontaneous  ionization  at  ordinary  temperatures,  20°  to  25°  C. 

EXPERIMENTAL  METHOD. 

Two  types  of  tubes  were  used  in  this  investigation.  In  the  first,  Fig. 
I,  A,  the  two  electrodes  a  and  b  were  of  the  same  material,  viz.,  nickel, 
and  of  the  same  dimensions.  In  the  second,  Fig.  2,  one  electrode,  b, 
consisted  of  the  alkali  metal,  potassium  or  caesium;  the  other,  a,  was  a 
disk  of  nickel. 

In  using  the  tube  of  the  first  type  potassium  was  placed  in  bulb  c 
(Fig.  i),  and  a  series  of  measurements  taken  when  the  field  was  from  a 
to  b,  and  also  for  the  field  from  b  to  a,  for  the  temperatures  25°,  50°,  and 
100°  with  the  tube  in  darkness.  Then  the  potassium  was  poured  into 
the  main  tube  and  lodged  between  the  electrodes,  but  not  in  contact  with 
either  of  them,  and  a  series  of  measurements  taken  for  25°,  50°,  100° 
and  150°  with  the  tube  in  darkness  and  also  with  a  beam  of  light  falling 
on  the  potassium,  but  not  on  the  electrodes. 

With  the  tube  of  the  second  type  (Fig.  2)  a  series  was  taken  with 
potassium  for  one  electrode  for  25°,  50°,  100°  and  150°  both  "in  darkness" 
and  with  the  "potassium  illuminated."  The  fourth  series  of  measure- 
ments were  taken  with  the  tube  of  the  second  type  and  with  caesium  for 
one  electrode  for  temperatures  of  25°,  40°,  70°  and  100°. 

1  Phys.  Zeits.,  12,  p.  398,  1911. 


242 


S.   HERBERT  ANDERSON. 


[VOL.  XXXV. 


EXPERIMENTAL  DETAILS. 

Construction  and  Preparation  of  the  Tubes, — Tube  No.  I  (Fig.  i,  A\ 
consisted  of  a  glass  tube  16  cm.  long,  3  cm.  in  diameter  at  the  middle. 
The  two  electrodes  were  nickel  disks  19  mm.  in  diameter  and  2  mm. 
thick.  The  distance  between  the  electrodes  was  2  cm.  Nickel  was  used 
for  the  electrodes  because  it  probably  contains  less  gas,  especially  oxygen, 
at  ordinary  temperatures  and  pressures  than  platinum  or  silver  and 
does  not  tarnish  very  readily. 

In  tube  No.  2,  Fig.  2,  the  bulb  was  4  cm.  in  diameter.  The  upper 
electrode  was  a  nickel  disk  19  mm.  in  diameter  and  2  mm.  thick.  The 
lower  electrode  was  potassium  for  one  set  of  experiments  and  caesium 


Fig.  1. 


Fig.  2. 


for  another.  The  area  of  the  potassium  was  about  the  same  as  that  of 
the  nickel  electrode;  and  of  the  caesium  about  I  cm2.  The  distance 
between  the  electrodes  was  2  cm. 

For  the  preparation  of  potassium  the  entire  tube  as  shown  in  Fig.  I 
was  used.  A  piece  of  potassium  was  introduced  into  the  tube  through 
an  opening  at  e  and  placed  at  d.  The  opening  at  e  was  then  closed, 
and  exhaustion  by  a  Gaede  pump  begun.  During  the  evacuation  the 
tube  A,  containing  the  electrodes,  was  enclosed  by  a  heating  coil  and 
kept  at  a  temperature  of  200°  C.  for  about  three  hours,  in  order  to 
remove  as  much  as  possible  the  gases  occluded  in  the  walls  of  the  tube 
and  in  the  electrodes,  so  that  on  subsequent  heating  gas  would  not  be 
given  off.  The  charcoal  bulb  /  was  heated  to  300°  or  400°  during  the 
exhaustion.  When  it  was  possible  to  pump  the  system  down  to  a  soft 
Rontgen  ray  vacuum  with  A  and  /  still  heated,  then  the  heating  coil 
was  removed  from  A  and  the  gas  flame  from  under  /  and  the  exhusation 
carried  to  a  hard  Rontgen  ray  vacuum.  The  vacuum  was  tested  by  a 
discharge  tube  not  shown  in  the  diagram.  The  potassium  was  melted 
and  the  oily  vapors  from  the  crust  pumped  out  during  the  melting. 
Potassium  was  then  distilled  into  the  bulb  g  in  the  following  manner: 


No.  4-1 


PROPERTIES   OF    VAPORS   OF  ALKALI   METALS. 


243 


On  carefully  heating  the  potassium  at  d  vapor  went  over  into  g  and 
metallic  potassium  deposited  on  the  walls  of  the  bulb.  The  tube  was 
then  allowed  to  cool  down  and  the  process  repeated.  In  this  way  suffi- 
cient potassium  could  be  collected  in  g.  The  surface  of  the  potassium 
obtained  in  this  manner  is  as  brilliant  as  polished  silver.  The  whole 
system  shown  in  Fig.  I  was  sealed  off  from  the  pump,  the  potassium 
poured  into  bulb  c  and  the  charcoal  bulb  placed  in  liquid  air.  After 
waiting  20  or  30  minutes  for  the  charcoal  to  absorb  the  remaining  gas 
the  tube  A  was  sealed  off  from  the  rest  of  the  system  at  h.  By  this 
method  of  preparing  a  tube  as  good  a  vacuum  as  possible  is  obtained. 

The  method  of  preparing  tube  No.  2,  Fig.  2,  was  the  same  except  that 
the  potassium  was  poured  into  the  tube  and  lodged  at  b  before  it  was 
sealed  off  from  the  rest  of  the  system. 

A  similar  method  was  used  in  preparing  tube  No.  2  with  caesium  for 
one  electrode,  but  with  the  following  modification:  the  tube  (Fig.  i)  was 
closed  with  a  rubber  stopper  at  e  and  exhausted.  Then  the  whole 
system  including  the  pump  was  filled  with  nitrogen  at  atmospheric 
pressure.  A  small  bulb  in  which  the  metallic  caesium  was  contained 
was  filled  with  nitrogen,  the  caesium  melted  and  poured  into  tube  at  e, 
which  was  then  closed  and  exhaustion  begun.  From  this  point  on  the 
method  of  preparing  the  tube  was  the  same. 

Arrangement  of  Apparatus  for  Measuring  Conductivity  at  Various  Tem- 
peratures.— The  method  used  for  measuring  the  conductivity  of  the  alkali 
vapor  is  shown  diagrammatically  in  Fig.  3.  The  tube,  either  No.  I  or 
No.  2,  was  placed  in  the  heating  coil  H,  which  was  enclosed  in  a  sheet- 
iron  box  C.  This  could  be  made  light  tight  and  the  experiment  was 
carried  on  in  a  dark  room. 
The  copper  core  of  the  coil 
and  the  sheet-iron  box  were 
both  grounded.  A  wire  from 
the  electrode  a  passed  through 
an  insulating  plug  and  was 
joined  to  a  movable  wire  W, 
which  made  connection  with 
a  water  rheostat  R.  To  the 
water  rheostat  were  connected 
the  terminals  of  a  storage  bat- 
tery Bi  of  1, 800  volts  and  one 
terminal  of  the  battery  was  grounded.  From  electrode  b  a  wire  passed 
through  an  insulating  plug  and  was  connected  to  one  pair  of  quadrants 
of  a  Dolezalek  electrometer.  The  other  pair  of  quadrants  was  grounded. 


244  5-   HERBERT  ANDERSON.  [VOL.  XXXV. 

k  is  a  plunger  key  by  which  the  electrode  b  and  the  pair  of  quadrants  to 
which  it  is  connected  may  be  grounded,  c  is  a  collar  of  metal  foil  placed 
around  the  tube  near  the  end  and  connected  to  earth  so  that  conduction 
over  the  outside  of  the  tube  may  be  avoided.  The  electrometer  and 
connecting  wires  were  enclosed  in  a  sheet-iron  box  D,  which  was  grounded. 

The  wire  connecting  electrode  b  to  the  electrometer  was  enclosed  in  a 
metal  tube  between  C  and  D  and  this  was  also  grounded.  The  scheme 
described  above  was  used  when  the  potential  of  electrode  b  was  to  be 
measured,  and  for  measuring  currents  of  the  order  io~13  to  io~n  amperes. 
When  currents  of  the  order  io~n  to  io~9  were  to  be  measured  one  terminal 
of  a  high  resistance  X  was  connected  to  the  wire  running  from  b  to  A 
at  e.  The  other  terminal  of  X  was  grounded.  When  k  was  opened  a 
current  flowed  from  b  through  X  to  the  earth  and  the  electrometer 
deflection  gave  the  fall  of  potential  across  this  resistance.  And  from 
these  two  quantities  the  current  can  be  computed.  When  currents 
greater  than  io~9  were  to  be  measured  the  wire  from  b  was  disconnected 
from  the  electrometer  at  e  and  connected  to  a  wire/  from  a  galvanometer. 
The  other  terminal  of  the  galvanometer  was  grounded. 

The  potential  applied  at  a  was  measured  by  one  of  three  electrostatic 
voltmeters  V  of  the  Kelvin  and  White  type.  Three  voltmeters  were 
necessary  to  cover  the  range  required  by  the  investigation ;  the  first  read 
from  o  to  90  volts,  the  second  from  100  to  600,  the  third  from  500  to  1,500. 

When  it  was  desired  to  pass  a  beam  of  light  into  the  tube  a  slit  in  the 
box  C  was  opened  which  was  in  line  with  the  slit  through  the  heating  coil. 

Heating  Coil. — The  tube  was  kept  at  a  temperature  higher  than  room 
temperature  by  means  of  a  heating  coil  or  electric  furnace.  The  core 
of  the  furnace  consisted  of  a  copper  cylinder  10  cm.  in  diameter  and  25 
cm.  long.  At  the  middle  of  the  cylinder  two  slits  were  cut  opposite  to 
each  other,  1.5  cm.  by  0.5  cm.,  through  which  a  beam  of  light  could  be 
directed  into  the  tube  placed  inside  the  coil.  The  winding  of  the  coil 
consisted  of  two  layers  of  wire  of  the  same  number  of  turns  so  connected 
that  the  magnetic  fields  of  the  two  layers  were  opposed.  With  this 
arrangement  the  magnetic  force  within  the  cylinder  was  found  to  be  so 
slight  as  not  to  effect  appreciably  the  movement  of  the  ions  in  the  tube. 

Galvanometer. — The  galvanometer  used  was  a  D'Arsonval  instrument 
manufactured  by  W.  G.  Pye,  Cambridge.  The  resistance  was  122  ohms, 
and  its  period  9  seconds.  The  deflections  were  read  by  a  telescope  and 
scale  at  a  distance  of  2.5  meters.  One  millimeter  deflection  indicated  a 
current  of  0.837  X  io~9  amperes. 

High  Resistance. — The  high  resistance  used  was  a  liquid  resistance, 
consisting  of  meta-xylol  with  a  few  drops  of  absolute  alcohol.  The 


No.  4.]  PROPERTIES   OF   VAPORS  OF  ALKALI   METALS.  245 

resistance  could  easily  be  changed  by  varying  the  proportion  of  meta- 
xylol  and  alcohol.  The  container  consisted  of  a  glass  tube  0.9  cm.  in 
diameter  and  8.0  cm.  long,  with  two  platinum  electrodes  sealed  through 
the  glass  3.5  cm.  apart.  The  tube  was  closed  by  a  ground  glass  stopper. 
The  resistance  was  observed  to  increase  with  the  time  probably  due  to 
evaporation  of  alcohol.  But  the  resistance  was  constant  for  a  period  of 
a  few  hours  required  for  a  set  of  readings.  The  resistance  used  varied 
from  4.72  X  io9  ohms  to  14.3  X  io10  ohms. 

EXPERIMENTAL  RESULTS. 

Tube  No.  I.  Potassium  in  Bulb  c. — The  first  series  of  measurements 
which  will  be  presented  were  taken  with  tube  No.  I  (Fig.  i,  A),  with 
the  potassium  in  bulb  c  and  with  the  tube  in  the  dark.  The  method  of 
taking  the  readings  was  as  follows :  The  potential  was  applied  at  electrode 
a  with  the  key  k  closed,  so  that  the  charge  which  would  arise  from  electro- 
static induction  in  electrode  b  and  connecting  wire  would  be  removed 
through  connection  to  earth  at  k.  Potentials  as  high  as  1,690  volts  were 
applied.  At  25°,  50°  and  75°  C.  nothing  of  the  character  of  a  regular  con- 
ductivity was  observed.  But  a  phenomenon  which  has  not  been  reported 
before  was  observed.  On  opening  the  key  k,  after  a  positive  potential  was 
applied  at  a  the  electrometer  gave  a  positive  deflection  which  very  soon 
came  to  a  maximum.  Then  there  was  a  negative  deflection  which  was 
nearly  of  a  constant  rate.  A  test  was  made  to  determine  whether  this  was 
due  to  a  charge  or  a  continuous  current.  With  +  100  volts  applied  at  a 
this  movement  of  the  electrometer  needle  toward  the  negative  continued 
for  three  hours  and  fifty  minutes,  and  the  rate  of  deflection  was  nearly 
constant  for  the  first  fifty  minutes.  After  the  maximum  negative  deflec- 
tion had  been  reached  the  electrometer  needle  drifted  toward  the  zero 
at  the  rate  of  0.5  mm.  per  minute,  which  was  about  the  rate  of  the  natural 
leak.  So  we  would  conclude  that  the  effect  is  of  the  nature  of  a  charge 
which  at  the  temperature  of  25°  builds  up  very  slowly  and  at  first  the  rate 
of  increase  is  a  linear  function  of  the  time. 

When  a  negative  potential  was  applied  the  results  were  similar  except 
that  the  directions  of  deflections  were  reversed.  It  was  also  observed 
that  if  a  higher  potential  was  applied  after  observations  had  been  made 
for  a  given  potential  the  "negative"  current  was  not  as  large  as  was  the 
case  when  a  period  of  rest  was  given  the  tube  with  both  electrodes 
grounded.  Consequently  it  was  found  necessary  in  taking  a  set  of 
readings  to  leave  the  tube  earthed  by  both  electrodes  for  io  minutes 
between  the  measurement  of  the  current  for  a  given  potential  and  the 
measurement  for  the  next  higher  potential.  Furthermore  it  was  noticed 


246 


5.    HERBERT  ANDERSON. 


[VOL.  XXXV. 


that  if  the  tube  was  exposed  to  light  while  a  potential  was  applied  at  a, 
there  was  a  larger  positive  deflection  and  after  the  light  was  turned  off 
the  "negative"  current  was  larger  than  before.  After  sufficient  time 
in  the  dark  the  "negative"  effect  decreased  to  a  constant  value. 

TABLE  I. 


"  Positive  "  Charge  and  "  Negative  "  Current 
at  25°. 

"  Positive  "  Charge  and  "  Negative  "  Current 
at  50°. 

Potential  in 
Volts. 

"  Positive  " 
Charge. 

"  Negative  " 
Current. 

Potential  in 
Volts. 

"Positive" 
Charge. 

"  Negative" 
Current. 

+     100 

+  4.3 

-0.4 

+     100 

+  2.5 

-     6.2 

300 

12.0 

1.2 

300 

6.5 

16.2 

500 

19.8 

2.0 

500 

14.0 

24.8 

700 

25.7 

2.8 

700 

18.0 

36.0 

900 

35.5 

3.5 

900 

20.5 

47.0 

1,100 

44.4 

4.5 

1,100 

25.0 

58.0 

1,300 



— 

1,300 

28.0 

72.0 

1,490 

off  scale 

5.5 

1,490 

32.0 

110.7 

1,690 

<<      .1 

6.2 

1,690 

off  scale 

111.0 

-    100 

-  3.8 

+0.47 

-    100 

-  2.5 

+     5.6 

300 

12.6 

1.2 

300 

7.5 

16.0 

500 

22.8 

1.9 

500 

12.0 

26.6 

700 

29.9 

2.55 

700 

16.5 

37.0 

900 

39.0 

3.0 

900 

21.0 

47.4 

1,100 

49.9 

3.6 

1,100 

25.0 

58.0 

1,300 

off  scale 

4.3 

1,300 

31.0 

66.0 

1,490 

n      « 

5.0 

1,490 

31.5 

84.0 

1,690 

<«      « 

5.2 

1,690 

39.0 

97.0 

Pi  'ftnl-  al 


Voi 


ml 


Fig.  4. 

In  Table  I.  there  are  given  data  which  show  the  relation  between  the 
potential  applied  and  the  "positive"  charge,  that  is,  the  first  electrometer 
deflection  after  opening  the  key,  which  is  in  the  same  direction  as  the 


No.  4-1 


PROPERTIES   OF    VAPORS   OF   ALKALI   METALS. 


247 


field;  and  also  the  relation  between  the  potential  applied  and  the  "nega- 
tive" effect,  which  is  a  current  appearing  after  the  "positive"  charge 
reaches  a  maximum  and  is  in  a  direction  opposite  to  the  field.  The 
"negative"  current  was  measured  by  the  rate  of  deflection  of  the  elec- 
trometer. The  "negative "  current  for  25°  and  50°  is  shown  by  the  curves 
of  Fig.  4.  For  the  curve  for  50°  the  ordinates  have  10  times  the  value 
that  they  have  for  the  curve  for  25°.  The  remarkable  feature  of  this 
phenomenon  is  that  even  with  a  potential  difference  of  1,700  volts  there  is  a 
current  in  the  opposite  direction  to  what  we  would  expect  from  our  present 
knowledge  of  conductivity. 

When  the  tube  was  heated  up  to  75°  the  "positive"  charge  did  not 
appear,  but  immediately  on  opening  the  key  there  was  a  "negative" 
deflection.  The  initial  negative  current  was  much  larger  than  at  lower 
temperatures,  but  the  effect  showed  more  the  character  of  a  charge  in 
that  it  came  to  a  maximum  much  sooner. 


t 


Fig.  5. 


Fig.  6. 


The  variation'of  the  initial  "negative"  current  and  of  the  charge  with 
the  temperature  is  shown  by  the  curves  of  Figs.  5  and  6  respectively.  In 
taking  the  readings  for  these  curves  a  constant  potential  of  +  400  volts 
was  maintained.  ,  It  was  impossible  to  measure  the  currents  for  tem- 
peratures higher  than  75°  by  this  method.  The  "  charge"  curve,  Fig.  6, 
shows  that  the  effect  reaches  a  maximum  between  65°  and  70°.  If  the 
curve  is  extended  until  it  cuts  the  axis  of  abscissae,  it  would  appear  that 
the  effect  disappears  at  about  104°; 

At  100°  when  the  potential  was  gradually  increased  up  to  +  700  volts 
a  reversal  of  the  electrometer  deflection  suddenly  occurred  and  there  was 
a  very  large  positive  deflection  accompanied  by  a  lighting  up  of  the  tube. 
There  is  then  at  this  temperature  and  pressure  a  conductivity  of  the 
usual  character  through  the  vapor. 

In  order  to  determine  whether  or  not  this  "negative"  effect  was  due 
to  anything  else  besides  the  potassium  vapor,  a  new  tube  was  made  of 
the  same  form  and  dimensions  in  which  no  potassium  was  present.  The 


248  5.   HERBERT  ANDERSON.  [VOL.  XXXV. 

new  tube  was  made  with  new  electrodes  and  from  new  glass  tubing 
thoroughly  cleaned.  The  cocoanut  charcoal  used  for  exhaustion  was 
freshly  burned.  The  tube  was  pumped  out  with  a  new  Gaede  pump 
which  had  never  been  used  for  the  exhaustion  of  tubes  where  alkali 
metals  were  present.  The  tube  was  pumped  out  to  a  hard  Rontgen  ray 
vacuum,  the  charcoal  bulb  immersed  in  liquid  air  for  about  20  minutes 
and  then  the  tube  was  sealed  off.  This  tube  showed  the  same  "  negative  " 
effect  as  the  one  with  potassium  vapor.  When  first  tried  immediately 
after  sealing  off,  it  gave  no  positive  deflection  when  a  positive  potential 
was  applied,  but  a  negative  deflection  the  rate  of  which  was  about  five 
times  as  great  as  that  observed  in  the  former  case.  After  leaving  in  the 
dark  and  grounded  by  both  electrodes  for  10  hours  there  was  then  ob- 
served, when  a  positive  potential  was  applied  and  the  key  opened,  first 
a  positive  charge  which  was  followed  by  a  negative  current  which  was 
smaller  than  the  one  observed  when  the  tube  was  first  tried.  When  a 
i6-candle-power  incandescent  lamp  shone  on  the  tube,  the  negative 
current  increased  and  the  positive  charge  entirely  disappeared.  After 
leaving  in  the  dark  for  a  few  hours  the  positive  charge  reappeared  and 
the  negative  current  decreased.  Hence  it  seems  that  this  phenomenon 
(i)  arises  from  the  glass  tube  or  the  me  tab  electrodes,  (2)  is  affected  by 
light,  (3)  is  diminished  by  the  presence  of  potassium  vapor.  Four  tubes 
with  similar  electrodes  of  nickel  and  containing  potassium  vapor,  one 
tube  with  nickel  electrodes  and  no  alkali  vapor,  and  one  tube  with 
aluminum  electrodes  and  no  alkali  vapor,  all  showed  the  same  phenomenon. 

No  attempt  is  made  at  this  time  to  explain  this  effect,  but  the  observa- 
tions made  are  presented  and  must  be  taken  account  of  in  measurements 
of  small  conductivities  through  gases. 

Tube  No.  I.  Potassium  between  the  Electrodes. — As  the  vapor  of 
potassium  shows  no  spontaneous  ionization  for  the  range  of  potentials 
and  temperatures  used,  the  next  problem  that  presents  itself  is  whether 
or  not  the  potassium  gives  off  particles  which  are  carriers  of  electricity. 
For  this  investigation  the  potassion  in  bulb  c  was  melted  and  poured 
into  the  main  tube  and  lodged  between  the  electrodes,  but  not  in  contact 
with  either  of  them.  Measurements  were  made  of  the  currents  for 
temperatures  25°,  50°,  100°  and  150°  with  the  tube  in  darkness  and  with 
the  potassium  illuminated  by  a  beam  of  light.  The  source  of  light  was  a 
i6-candle-power  incandescent  carbon  filament  lamp,  supplied  from  a 
storage  battery  of  120  volts.  The  beam  of  light  did  not  fall  on  the  nickel 
electrodes,  though  of  course  some  reflected  light  did  reach  them.  The 
results  obtained  are  shown  by  the  curves  of  Fig.  7.  The  curves  with 
solid  lines  represent  the  currents  with  the  "potassium  in  darkness,"  those 


No.  4.] 


PROPERTIES   OF   VAPORS   OF  ALKALI   METALS. 


249 


with  broken  lines  represent  the  curves  with  the  "potassium  illuminated." 
Attention  is  called  to  four  particulars  of  these  curves:  (i)  the  "nega- 
tive" effect  persists  for  25°  and  50°  in  darkness  and  is  the  same  order  of 
magnitude  as  occurred  when  the  potassium  was  in  bulb  c\  this  disappears 
for  100°  in  darkness  and  is  not  apparent  for  any  of  the  temperatures  tried 


11  VOLTS. 

Fig.  7. 

when  the  potassium  is  illuminated ;  (2)  the  linear  character  of  the  curve 
for  1 00°  in  darkness  and  the  abrupt  bend  in  the  negative  branch  at  875 
volts;  (3)  for  25°,  50°  and  100°,  "potassium  illuminated,"  the  positive 
branches  of  the  curves  show  larger  currents  than  the  negative;  (4)  for 
1 00°  and  150°  there  is  a  negative  current  when  no  potential  is  applied. 
These  peculiarities  can  be  better  explained  later  after  the  presentation 
of  the  phenomena  of  tube  No.  2. 

Tube  No.  2.  Potassium. — This  tube  gives  more  nearly  than  tube  No.  I 
the  conditions  that  are  realized  in  a  photo-electric  cell  prepared  for 
determining  the  maximum  positive  potentials  assumed  by  a  metal  under 
the  action  of  light.  The  conductivity  was  measured  with  the  tube  "in 
darkness"  and  with  the  "potassium  illuminated"  at  the  temperatures 
of  25°,  50°,  100°  and  150°.  The  results  are  shown  by  the  curves  of  Fig.  8. 


250 


5.   HERBERT  ANDERSON. 


[VOL.  XXXV. 


The  solid  lines  represent  the  currents  with  the  "potassium  in  darkness," 
the  broken  lines  the  currents  with  the  "potassium  illuminated."  For 
both  of  the  curves  for  150°  the  ordinates  have  10  times  the  value  marked 
on  the  figure,  that  is,  the  unit  is  io~9  instead  of  io~10,  which  applies  to  the 
other  curves. 

One  of  the  most  interesting  points  brought  out  by  this  series  of  measure- 
ments is  the  existence  of  a  negative  current  when  no  electric  field  is 


5/7 

'§!; 

AD 

;/ 

i 

^ 

10 

2 

* 

*L 

20 

^1 

/ 

lOilff" 

/ 

2 

F 

X 

.X 

•>*"" 

,:S-- 

, 

,  d 

/ 

2S'  d 

00 

5 

i 

2. 

A? 

^ 

ID 

^-^"2 

V 

^ 

» 

6 

«? 

'    u 

\ 

r^<! 

r^x' 

20 

t 

rX 

30 

f 

SO 

Fig. 

VOLT 
8. 

5. 

applied;  that  is,  there  is  a  positive  current  from  b  to  a,  Fig.  2,  from  the 
potassium  electrode  to  the  nickel  electrode.  This  phenomenon  was 
observed  and  has  been  investigated  by  J.  W.  Woodrow1  in  this  laboratory. 
This  effect  is  apparent  at  25°  in  darkness  and  at  50°,  100°  and  150°  with 
the  potassium  illuminated  as  well  as  in  darkness.  Woodrow  found  this 
effect  characteristic  of  the  alkali  metals.  This  effect  for  potassium  and 
caesium  is  shown  by  the  curves  of  Figs.  9  and  10.  The  curves  of  Fig.  9 
show  how  the  negative  charge  on  the  potassium  or  caesium  increases  with 
the  time.  In. order  to  obtain  the  readings  for  these  curves  the  alkali 
metal  electrode,  6,  was  connected  to  the  electrometer  and  a  was  earthed. 
The  curves  of  Fig.  10  show  the  increase  of  the  current  with  the  tempera- 
ture. (The  ordinates  for  the  potassium  curve  have  a  larger  value  than 
for  the  caesium  curve.)  These  curves  are  introduced  here  because  of 
IPHYS.  REV.,  XXXV.,  p.  203,  1912. 


No.  4.] 


PROPERTIES  OF   VAPORS  OF  ALKALI   METALS. 


251 


their  bearing  upon  the  author's  results  and  as  a  confirmation  of  Woodrow's 
observations. 

The  second  point  of  interest  of  this  tube  is  that  at  25°  "in  darkness," 
when  a  given  potential  is  applied  at  a,  the  current  occurring  is  not  con- 


Fig.  9. 

stant.  This  is  shown  by  the  curves  of  Fig.  n.  Curve  B  shows  how 
the  current  varies  when  +  300  volts  is  applied,  and  curve  B'  when  —  300 
volts  is  applied.  B'  could  not  be  carried  farther  as  the  deflections  went 


Fig.  10. 

off  the  scale.  When  no  potential  is  applied,  that  is,  when  a  is  grounded 
and  b  is  connected  to  the  electrometer  the  negative  current,  mentioned 
above,  decreases  as  the  charge  on  the  electrode  b  builds  up.  This  is  shown 


252 


5.   HERBERT  ANDERSON. 


[VOL.  XXXV. 


by  curve  A.  When  the  ordinates  of  A  are  subtracted  algebraically  from 
those  of  B  and  B'  two  curves  C  and  C'  respectively  are  obtained  which  are 
almost  identical,  except  that  ordinates  are  of  opposite  sign.  Hence  it 


'G 


Fig.  11. 

would  appear  that  the  difference  between  B  and  B'  is  due  to  the  effect 
of  4. 

The  equation  of  a  curve  of  the  type  of  C  and  C'  is  of  the  form 


+ 


+  C. 


The  constants  of  this  equation  can  be  obtained  by  taking  values  of 
i  for  five  different  values  of  t  and  thus  getting  five  equations  with  the  five 
unknowns  A,  B,  C,  a,  and  b.  The  actual  values  of  these  constants  are 
of  no  consequence  as  they  will  give  us  no  further  information  of  the 
nature  of  the  phenomenon;  so  the  determination  of  the  constants  was 
carried  out  only  far  enough  to  see  that  all  five  constants  are  real  and 
different  from  zero.  These  curves  then  may  be  represented  by  an  equa- 
tion of  this  form.  From  this  fact  we  may  conclude  that  there  are  three 
distinct  effects  occurring  in  the  tube  in  addition  to  the  current  of  curve 
A  :  (i)  a  positive  current  which  decreases  according  to  the  equation 


(2)  a  negative  current  decreasing  according  to 

i  =  Be~bt, 


No.  4.]  PROPERTIES   OF   VAPORS  OF  ALKALI  METALS. 

(3)  and  a  constant  current  given  by 

«  =  C. 

TABLE  II. 

Tube  No.  2,  Ctesium. 
Temperature  25°. 


253 


In  Darkness. 

Caesium  Illuminated. 

Potential  in  Volts. 

Current  in  Amperes. 

Potential  in  Volts. 

Current  in  Amperes. 

0 

-  1.83X10-12 

0 

+     0.58  X  10-" 

+     200 

+  1.502 

+     100 

10.56 

-    400 

3.34      . 

300 

15.4 

600 

6.44 

500 

18.0 

800 

11.27 

700 

21.5 

1,000 

16.85 

900 

24.1 

1,200 

23.85 

1,000 

25.4 

1,400 

33.5 

1,640 

192.0 

1,600 

38.3 

1,650 

40.2 

-    200 

-  3.35 

-    200 

-     0.963 

400 

5.47 

400 

1.26 

600 

8.52 

600 

1.705 

800 

13.6 

800 

2.295 

1,000 

20.2 

1,000 

3.37 

1,200 

30.1 

1,200 

4.77 

1,400 

47.0 

1,400 

7.03 

1,600 

11.5 

1,650 

13.2 

Temperature  40°. 


0 

-  5.94  X10~12 

0 

+  0.222  X  10-" 

+  100 

2.58 

+  10 

14.2 

200 

1.29 

88 

23.1 

300 

1.4 

410 

83.7 

400 

+  6.87 

500 

543.0 

500 

16.8 

600 

22.6 

625 

60.2 

-  100 

-  7.76 

-   12 

-  4.82 

200 

9.9 

57 

6.33 

300 

19.5 

100 

8.15 

400 

41.2 

200 

8.7 

600 

837.0 

300 

11.85 

366 

25.6 

550 

83.7 

600 

234.0 

254 


5.   HERBERT  ANDERSON. 


[VOL.  XXXV. 


TABLE  II. — Continued. 

Temperature  70°. 


In  Darkness. 

Caesium  Illuminated. 

Potential  in  Volt». 

Current  in  Amperes. 

Potential  in  Volts. 

Current  in  Amperes. 

0 

-  14.0  X10-10 

0 

-     0.036  X10-10 

+     100 

1.2 

+     100 

+     1.88 

200 

+  15.6 

200 

2.48 

300 

78.8 

300 

3.35 

370 

232.0 

400 

83.7 

500 

167.5 

-    100 

-     0.293 

-    100 

-     0.547 

200 

0.58 

197 

2.53 

300 

1.7 

300 

14.2 

321 

2.53 

400 

25.05 

420 

217.0 

500 

201.0 

Temperature  100°. 


0 

-  0.5  X10-10 

0 

-  0.248X10~10 

+  100 

+  0.1 

+  100 

1.43 

200 

0.9 

190 

2.68 

300 

2.64 

300 

12.55 

400 

10.05 

400 

20.05 

500 

23.4 

500 

38.2 

600 

134.0 

600 

41.8 

665 

655.0 

800 

100.5 

1,000 

309.0 

-  100 

-  1.09 

-  100 

-  1.6 

200 

2.25 

200 

4.18 

300 

3.35 

300 

8.37 

400 

10.9 

400 

16.75 

500 

25.01 

600 

67.0 

600 

45.2 

800 

159.0 

700 

75.3 

1,000 

259.0 

825 

250.5 

Curves  B  and  Bf  are  typical  of  all  those  taken  for  various  potentials. 
For  negative  potentials  of  500  volts  of  more  the  initial  current  is  positive; 
this  decreases  and  is  followed  by  a  negative  current  which  increases  to 
a  maximum  and  then  decreases. 

The  features  of  the  curves  of  Fig.  8  to  which  attention  will  be  called 
later  are:  (i)  with  the  "potassium  illuminated"  all  the  curves  obtained 
when  a  positive  potential  was  applied  at  a  show  the  characteristics  of 
ionization  curves,  though  saturation  is  not  clearly  marked ;  (2)  the  nega- 
tive branch  of  the  curve  for  "potassium  illuminated"  at  25°  shows  prac- 
tically no  current;  (3)  the  abrupt  bend  away  from  the  axis  of  abscissae 


No.  4.]  PROPERTIES  OF   VAPORS   OF  ALKALI  METALS.  255 

in  all  the  curves  obtained  when  a  negative  potential  was  applied;  (4) 
the  curves  "in  darkness"  and  "potassium  illuminated"  very  nearly 
coincide  for  the  negative  branches  of  the  curves  at  100°,  and  for  both  the 
positive  and  negative  branches  of  the  curves  at  150°. 

Tube  No.  2.  Ccesium. — The  observations  in  this  series  were  carried 
out  in  the  same  manner  as  for  tube  No.  2,  potassium,  except  that  the 
temperatures  used  were  25°,  40°,  70°  and  100°.  The  results  are  given 
in  the  data  of  Table  II.  No  curves  are  shown  because  they  differ  in  no 
essentials  from  those  for  potassium,  Fig.  8.  The  following  features  are 
worth  noting:  (i)  the  existence  of  a  negative  current  when  no  field  is 
applied,  as  with  the  potassium,  due  to  the  emission  of  positive  particles 
from  the  caesium ;  (2)  the  great  increase  in  the  current  at  25°  and  40° 
when  the  caesium  was  illuminated  over  the  currents  occurring  when  the 
caesium  was  in  darkness. 

DISCUSSION  OF  RESULTS. 

The  experiment  with  tube  No.  I  with  potassium  alone  between  the 
electrodes,  that  is,  with  the  solid  potassium  in  bulb  c,  Fig.  I,  shows  that 
there  is  nothing  of  the  character  of  a  spontaneous  ionization  at  a  tem- 
perature as  high  as  75°.  No  conductivity  of  the  usual  type  was  observed 
when  a  potential  of  1,700  volts  was  applied.  At  a  temperature  of  100° 
when  the  potential  is  gradually  increased  there  is  a  luminous  discharge 
at  700  volts.  But  there  is  no  current  before  this  occurs.  The  abruptness 
of  the  discharge  indicates  that  there  are  no  ions  present  until  produced 
at  this  instant.  At  this  temperature,  100°,  the  velocity  of  agitation  is 
relatively  large.  Some  molecules  acquire  sufficient  velocity  so  that  when 
a  collision  with  another  molecule  occurs  the  electron  system  of  the  atom 
is  put  in  such  an  unstable  condition  that  the  electric  force  due  to  the  700 
volts  difference  of  potential  between  the  electrodes  is  sufficient  to  drag  an 
electron  from  the  atom  and  ionization  occurs.  The  ions  thus  produced 
acquire  sufficient  velocity  under  the  action  of  the  electric  field  to  produce 
ionization  by  collision  and  the  luminous  discharge  occurs. 

The  absence  of  spontaneous  ionization  is  further  verified  by  the  fact 
that  when  in  tube  No.  I  the  potassium  was  introduced  into  the  tube 
so  as  to  lie  between  the  electrodes  no  conductivity  of  the  usual  type  oc- 
curred until  the  temperature  was  raised  to  100°. 

Woodrow  found  that  the  alkali  metals  in  the  dark  gave  off  positive 
particles  and  that  the  current  arising  therefrom  increased  with  the 
temperature  according  to  the  relation 

i  =  aTe-b», 


256  5.   HERBERT  ANDERSON.  [VOL.  XXXV. 

where  a  and  b  are  constants  and  T  the  absolute  temperature  (see  curves 
of  Fig.  10).  This  will  be  used  as  a  basis  for  explaining  the  peculiarities 
of  the  curves  of  Fig.  8,  to  which  attention  was  called  earlier. 

The  curve  for  100°  "in  darkness"  is  a  straight  line  up  to  1,600  volts. 
It  does  not  seem  reasonable  to  assume  that  this  is  a  portion  of  an  ioniza- 
tion  curve  or  saturation  would  be  reached  before  1,600  volts.  Since 
positive  particles  are  given  off  from  the  liquid  potassium  at  this  tempera- 
ture in  some  considerable  numbers,  we  may  assume  that  from  the  surplus 
of  electrons  left  in  the  metal  some  will  be  given  off  under  the  action  of 
the  field  between  the  electrodes.  When  equilibrium  is  reached  the  same 
number  of  positive  and  negative  particles  will  be  given  off  and  there  will 
be  a  steady  current.  The  number  of  particles  given  off  will  increase  with 
the  field  and  if  the  relation  is  a  linear  one  the  curve  is  explained.  Since 
in  all  probability  the  positive  ions  are  atoms  of  potassium,  potassium 
will  be  deposited  on  electrode  b.  If  this  is  the  case  the  other  peculiarities 
of  the  curves  of  Fig.  7  can  be  explained. 

After  this  curve  is  taken  with  the  positive  potential  the  curve  with 
the  negative  potential  is  taken  at  the  same  temperature.  Now  with 
the  field  in  this  opposite  direction  to  what  it  was  formerly  positive 
particles  will  be  given  off  from  the  layer  of  potassium  on  electrode  b  in 
addition  to  positive  and  negative  particles  given  off  from  the  potassium 
in  the  tube.  The  direction  of  the  field  will  facilitate  the  natural  tendency 
of  the  potassium  to  give  off  positive  particles.  This  accounts  for  the 
fact  that  in  the  negative  branch  of  the  curve  for  100°  "in  darkness"  the 
currents  are  a  little  larger  than  in  the  positive  branch.  Furthermore 
at  875  volts  there  is  an  abrupt  bend  in  the  curve  showing  ionization  by 
collision.  At  this  potential  the  positive  particles  acquire  sufficient 
velocity  to  ionize  the  vapor.  And  increase  of  ionization  is  very  rapid 
when  positive  ions  begin  to  produce  ionization  by  collision. 

For  150°  the  order  of  taking  observations  was  the  same  as  for  100°  and 
this  would  result  in  a  greater  deposit  of  potassium  on  electrode  b.  The 
negative  branch  of  the  curve  "in  darkness"  becomes  parallel  to  the 
current  axis  for  a  lower  potential  than  the  positive  branch.  And  this  is 
accounted  for  by  the  fact  that  positive  particles  are  given  off  from 
electrode  b  when  the  field  is  in  this  direction. 

Attention  has  been  called  to  the  fact  that  for  25°,  50°  and  100°  the 
positive  branches  of  the  curves  for  "potassium  illuminated"  give  larger 
values  for  the  currents  in  the  linear  portions  of  the  curve  than  do  the 
negative  branches.  This  can  be  explained  also  by  assuming  that  there  is 
some  potassium  deposited  on  b.  For  when  the  direction  of  the  field  is 
from  a  to  b  under  the  action  of  reflected  light  electrons  will  be  given  off, 


No.  4.] 


PROPERTIES   OF   VAPORS   OF  ALKALI   METALS. 


257 


while  they  will  not  be  given  off  so  readily  when  the  field  is  from  b  to  a. 

The  negative  current  at  100°  and  150°  with  no  field  present  may  also 
be  explained  by  the  deposit  of  potassium  on  electrode  b. 

Of  course  this  deposit  of  potassium  on  b  is  of  no  vital  importance  in  the 
investigation,  but  the  peculiarities  of  the  curves  of  Fig.  7  are  very  reason- 
ably explained  by  this  fact. 

Attention  previously  has  been  called  to  the  fact  that  some  of  the 
curves  of  Fig.  8,  taken  with  tube  No.  2,  potassium,  show  the  character- 
istic features  of  ionization  curves,  viz.,  (i)  a  straight  line  where  the 
current  obeys  Ohm's  law,  followed  by  a  bending  toward  the  axis  of 
abscissae,  (2)  a  portion  parallel  to  the  axis  of  abscissae  where  saturation 
occurs,  (3)  a  rapid  rise  away  from  the  axis  of  abscissae  where  ionization 
by  collision  begins.  The  curves  obtained  differ  from  the  ionization  curve 
above  described  in  that  at  no  point  does  the  curve  become  parallel  to 
axis  of  abscissae.  This  is  due  to  the  source  of  ions.  In  order  to  have  a 
portion  of  the  curve  parallel  to  the  axis  of  abscissae,  the  source  of  ions 
must  be  such  that  the  rate  of  producing  these  primary  ions  is  constant. 
This  is  the  case  where  the  gas  is  ionized  by  Rontgen  rays  or  a  radioactive 
substance.  In  this  experiment  the  source  of  the  ions  is  the  photo-electric 
action  of  the  potassium,  and  the  rate  of  production  increases  with  the 
potential  applied.  This  accounts  for  the  straight  line  portion  of  the  curve 
seen  in  the  curves  of  Fig.  8.  The  point  where  the  curve  begins  to  bend 
away  from  the  straight  line  corresponds  to  the  potential  where  ionization 
by  collision  begins.  In  the  curves  taken  at  100°  and  150°  the  straight 
line  portion  of  the  curve  is  not  so  apparent  because  at  these  temperatures 
ionization  by  collision  begins  at  a  lower  potential. 

TABLE  III. 

In  Darkness. 


Current. 

o  Volts. 

ioo  Volts. 

aoo  Volts. 

300  Volts. 

400  Volts. 

25° 

-     0.0283  X  10-" 

-     0.035 

-         0.055 

-       0.071 

-  0.101 

50° 

-     0.59 

-     0.556 

-        0.47 

0.38 

-  0.4 

100° 

-  44.0 

-  22.0 

-        1.56 

+      15.0 

+30.0 

150° 

-244.0 

+670.0 

+  1,780.0 

+2,760.0 

off  scale. 

Potassium  Illuminated. 


Current. 

/p                       *. 

o  Volts. 

ioo  Volts. 

aoo  Volts. 

300  Volts. 

400  Volts. 

25° 

-  0.075  X10~10 

+  3.2 

+     5.0 

+     6.5 

+       8.7 

50° 

-  0.242 

+  2.6 

+     5.0 

+  10.5 

+      28.5 

100° 

-  4.3 

+  2.3 

+    9.6 

+  23.8 

+      58.5 

150° 

-21.0 

+70.0 

+  158.0 

+250.0 

+  1,010.0 

258 


HERBERT  ANDERSON. 


[VOL.  XXXV. 


The  curves  taken  with  caesium  are  similar  to  those  with  potassium. 
The  negative  branch  of  the  curve  taken  at  25°  with  the  "potassium 
illuminated"  shows  practically  no  current  of  the  same  magnitude  as  the 
other  curves.  This  is  what  would  be  expected ;  for  with  the  field  in  that 
direction  no  electrons  would  be  given  off.  Any  current  that  occurs  must 
be  due  to  the  positive  particles.  It  is  reasonable  to  expect  that  if  a 

higher  voltage  had  been  applied 
there  would  have  occurred  an 
abrupt  bend  as  in  the  curve  for 
50°.  Such  a  bend  occurs  where 
the  positive  particles  acquire 
sufficient  velocity  to  produce 
ionization  by  collision. 

The  close  agreement  of  the 
curves  for  "in  darkness"  and 
"potassium  illuminated"  in  the 
negative  branches  for  100°  and 
150°  shows  that  the  source  of 
ions  must  be  the  positive  par- 
ticles whose  expulsion  from  the 
potassium  is  independent  of  the 
action  of  light. 

It  is  rather  remarkable  that 
for  the  curves  for  50°,  100°  and 
150°  the  abrupt  bend  occurs  at 
the  same  potential  very  nearly, 
350  volts.  This  indicates  that 
the  velocity  acquired  to  produce  ionization  by  collision  is  due  to  the 
electrical  field  almost  entirely  and  that  the  initial  velocity  for  all  tem- 
peratures is  small  compared  to  this. 

In  order  to  show  how  the  currents  obtained  with  tube  No.  2,  with 
electrode  b  of  potassium  vary  with  the  temperature  we  may  plot  tempera- 
tures as  abscissae  for  a  given  potential.  These  curves  are  given  in  Fig.  12, 
and  the  data  for  them  in  Table  III. 

The  solid  lines  represent  currents  measured  with  the  potassium  "in 
darkness."  The  portions  of  the  curves  represented  by  dots  and  dashes 
have  been  determined  only  in  a  qualitative  way.  Reference  to  the  table 
will  show  that  there  is  some  warrant  for  drawing  them  as  they  are.  The 
curves  of  broken  lines  represent  the  currents  measured  with  the  "potas- 
sium illuminated."  The  ordinates  for  the  latter  have  40  times  the  value 
of  the  former.  For  all  these  curves  the  field  is  from  a  to  b,  so  that  the 


Fig.  12. 


No.  4.]  PROPERTIES   OF   VAPORS   OF  ALKALI   METALS.  259 

positive  currents  are  due  to  electrons  given  off  from  the  potassium  or  to 
ions  produced  by  them,  while  the  negative  currents  are  due  to  the  positive 
particles.  The  curves  show  that  for  temperatures  up  to  50°  for  the 
potassium  in  darkness  the  emission  of  positive  particles  is  predominant 
for  all  potentials.  But  for  higher  temperatures  the  emission  of  electrons 
is  predominant  for  potentials  of  300  volts  and  more.  It  is  quite  likely 
that  the  critical  temperature  is  the  melting  point  of  potassium,  62°. 

If  the  curve  for  o  potential,  "potassium  illuminated,"  were  plotted 
on  the  same  scale  as  the  curve  for  o  potential,  "potassium  in  darkness," 
it  would  be  seen  that  the  two  very  nearly  coincide,  as  the  data  of  the 
table  show.  This  means  that  the  -electron  current  due  to  the  photo- 
electric effect  is  very  small  compared  to  the  emission  of  positive  particles 
from  the  potassium  at  higher  temperatures.  The  greatest  relative 
difference  between  the  two  effects  is  at  25°.  At  this  temperature  when 
the  light  is  applied  the  current  changes  from  a  small  negative  value  to  a 
positive  value  25  times  greater.  But  for  higher  temperatures  the  result- 
ing current  is  negative  both  with  and  without  light  and  the  difference 
between  the  two  currents  is  only  of  a  few  per  cent.  However,  when  a 
field  is  applied  from  a  to  b  then  the  electron  current  becomes  predominant. 

QUANTITATIVE  RESULTS. 

Ratio  of  the  Number  of  Electrons  Given  off  to  the  Number  of  Atoms  Present. 
— From  the  electron  current  occurring  when  the  potassium  is  illuminated 
either  with  or  without  an  applied  potential,  the  number  of  electrons  leaving 
wither  with  or  without  an  applied  potential,  the  number  of  electrons 
leaving  the  surface  of  the  alkali  metal  per  second  can  be  computed  and 
compared  with  the  number  of  atoms  in  the  active  layer.  At  25°  the 
negative  current  for  potassium  in  darkness  with  zero  potential  is  0.283  X 
io~12  amperes.  And  the  positive  current  when  the  potassium  is  illumi- 
nated is  7.5  X  io~12  amperes.  Since  the  positive  current  must  be  the 
difference  between  the  current  due  to  the  electrons  and  that  due  to  the 
positive  particles,  the  current  of  electrons  must  be 

7.5    X  io-12  +  0.283  X  io~12  =  7783.X  io~12  amperes, 
7.78  X  io~12  amp.  =  7.78  X  io~13  e.m.  units. 

The  number  of  electrons  reaching  the  electrode  per  second  is 

7.78  X  io-13 

i^xl^o  -  5-02  X  i*  ,    :,      ,,,:i_ 

where  1.55  X  io~20  is  the  value  of  e  in  electromagnetic  units. 

The  potassium  was  in  the  shape  of  a  disk  with  a  very  nearly  flat 
surface  and  a  radius  of  about  I  cm. 


26O  5.   HERBERT  ANDERSON.  [VOL.  XXXV. 

Area  of  potassium  =  xi2  =  3.1416  cm2. 
Diameter  of  potassium  atom  =  4.74  X  io~8  cm. 
Cross-sectional  area  occupied  by  one  potassium  atom  is 

(4.74  X  io-8)2  =  2.25  X  io~15  cm2. 

3.1416 
Number  of  atoms  in  one  layer  =  --  —  -  —6  =  1.397  X  io15. 

2.25      /N      IO 

Ladenburg1  has  found  that  the  thickness  of  the  layer  of  metal  effected 
by  light  is  about  io~4  cm.  Hence  the  number  of  layers  of  atoms  of 
potassium  in  the  active  layer  of  the  metal  is  given  by 


io 


-4 


=  2.  II    X   IO3. 


4.74  X 
The  total  number  of  atoms  in  the  active  layer  is 

1.397  X  io15  X  2.1 1  X  io3  =  2.95  X  io18. 
Ratio  of  number  of  atoms  to  number  of  electrons  given  off  per  second  is 

^4^  =  5-88  X  io-      ,  !*; 

5.02  X  io7 

That  is,  one  atom  out  of  5.88  X  io10  gives  out  one  electron  per  second. 
At  this  rate  it  would  require  5.88  X  io10  seconds  or  1,860  years  for  each 
atom  to  give  out  one  electron.  Of  course  the  electron  current  can  be 
considerably  increased  by  using  a  more  intense  light  and  one  of  shorter 
wave-length.  And  then  the  ratio  between  the  number  of  atoms  and 
the  number  of  electrons  given  off  will  be  much  decreased.  But  this 
computation  serves  to  emphasize  the  fact  that  the  number  of  atoms 
effected  is  exceedingly  small.  This  may  be  due  to  one  of  two  causes,  or 
possibly  to  both:  (i)  only  a  very  few  of  the  atoms  are  in  condition  to 
give  out  electrons  under  the  influence  of  light;  (2)  light  has  a  structure 
and  the  energy  is  not  uniformly  distributed  over  the  light  wave  front, 
but  is  concentrated  along  certain  lines  as  suggested  by  the  theory  of 
J.  J.  Thomson2  and  amplified  by  Kunz.3  In  this  investigation  there  is 
some  evidence  in  favor  of  the  first  explanation.  A  comparison  of  the 
curves  for  "potassium  illuminated"  and  "in  darkness"  in  Fig.  8  will 
show  that  as  the  temperature  increases  the  effect  of  light  on  the  current 
becomes  less  and  less,  until  at  150°  the  curves  for  "potassium  illuminated  " 
and  ' '  in  darkness ' '  almost  coincide.  That  is ,  at  this  temperature  electrons 
are  given  off  just  as  readily  without  light  as  with  it  when  an  electric  field 
is  applied,  or  the  photo-electric  action  at  this  temperature  is  practically 

1  Ann.  der  Phys.,  12,  p.  558,  1903. 

1  Proc.  of  Camb.  Phil.  Soc.,  14,  pt.  4,  p.  41,  1908. 

8  PHYS.  REV.,  29,  p.  212,  1909. 


No.  4.]  PROPERTIES  OF   VAPORS  OF  ALKALI   METALS.  26 1 

zero.  Hence  it  appears  that  the  electron  current  depends  more  upon 
the  condition  of  the  metal  than  of  the  incident  light.  If  the  number  of 
electrons  given  off  depended  alone  on  the  structure  of  light,  the  electron 
current  should  be  much  larger  with  light  than  without  light  for  all 
temperatures. 

At  150°  with  +  100  volts  potential  the  current  is  about  1,000  times 
larger  than  at  25°  and  with  zero  potential.  But  even  with  this  current 
the  ratio  between  the  number  of  atoms  and  the  number  of  electrons 
given  off  is  a  large  one,  5.88  X  io7.  So  that  even  at  this  temperature 
the  number  of  atoms  in  condition  to  give  off  electrons  is  small. 

Estimate  of  the  Maximum  Vapor  Pressure  Possible  of  Potassium. — 
When  light  is  incident  on  a  metal  the  electrons  are  given  off  with  a 
velocity  which  can  be  obtained  by  the  relation 

Pe  =  %mv2, 

where  e  is  the  charge  of  the  electron  and  P  the  maximum  positive  poten- 
tial assumed  by  the  metal  in  the  photo-electric  action.  The  maximum 
velocity  of  the  electrons  from  potassium  in  this  work  when  zero  potential 
was  applied  is  due  to  the  shortest  wave-length  of  visible  light,  about 
X  4,200.  D.  W.  Cornelius  in  this  laboratory  found  the  velocity  due 
to  this  wave-length  to  be  6.21  X  io7  cm.  per  second.  When  there  is  an 
electric  field  acting  the  velocity  of  the  electrons  increases  beyond  the 
initial  velocity  until  the  electron  has  sufficient  velocity  to  produce  an 
ion  by  collision.  This  relation  is  expressed  by 

W  =  Eel  +  Yzmv*, 

where  W  is  the  energy  required  to  produce  an  ion,  E  the  electric  field, 
e  the  elementary  electrical  charge,  m  the  mass  of  the  electron,  v  the 
initial  velocity  and  /  the  distance  from  the  surface  of  the  metal  that  the 
electron  must  go  to  gain  sufficient  velocity  to  produce  ionization.  The 
value  of  E  can  be  taken  from  the  curve  at  the  point  of  departure  from 
a  straight  line.  From  the  curve  for  25°,  Fig.  8,  we  find  the  potential 
corresponding  to  this  point  of  departure  to  be  350  volts.  As  the  elec- 
trodes were  2  cm.  apart,  the  value  of  E  is 

35° 

-  =  175  volts  per  cm., 


E  =  —  =  0.583  e.s.  units  per  cm., 

e  =  4.65  X  io-10, 
m  =  8.7  X  io-28, 
v  =  6.21  X  io7. 


262  5.   HERBERT  ANDERSON.  [VOL.  XXXV. 

The  value  of  Wis  taken  at  1.58  X  io~n  ergs,  which  is  the  value  obtained 
by  Bishop1  for  hydrogen  and  also  by  Kemp  in  this  laboratory.  So  far 
as  has  been  investigated  this  value  does  not  vary  very  much  for  different 
gases,  so  it  will  be  assumed  that  it  is  a  reasonable  value  for  potassium 

vapor. 

8.7  X  io~28(6.2i  X  io7)2 


Ee  5.83  X  io-1  X  4.65  X  io~1( 

_  1-58  X  io~n  -  0.169  X  io~n 
2.71  X  io-10 

=  5.2  X  io~2  cm. 

Now  the  mean  free  path  of  the  molecules  of  potassium  vapor  must 
be  at  least  this  great  or  there  could  be  no  ionization  by  collision  at  this 
field  strength.  Assuming  this  to  be  the  minimum  mean  free  path  we  can 
calculate  the  maximum  number  of  molecules  per  cm3.  The  mean  free 
path  is  given  by 


"1/27TWC72  ' 

where  n  is  the  number  of  molecules  per  cubic  centimeter  and  a  is  the 
diameter  of  the  molecule.     We  have  then 


V/27r/o-2       V  2*5.2  X  io-2(474  X 
=  1.925  X  io15. 

We  may  assume  that  at  the  temperature  and  pressure  existing  in  the  tube 
the  potassium  vapor  acts  as  a  perfect  gas  and  so  compute  the  pressure 
from 

P  =  p«Tn 


where  P0  =  760  mm.  pressure,  TQ  =  273°,  w0  the  number  of  molecules  in 
a  cubic  centimeter  of  gas  at  standard  conditions  and  is  equal  to  2.72  X  io19, 
T  the  absolute  temperature  of  the  vapor  and  n  the  number  of  molecules 
of  the  vapor  per  cubic  centimeter.  Hence 

760  X  298  X  1.925  X  io15 
273  X  2.72  X  io19 

=  0.0587  mm. 
REV.,  33,  p.  325,  1911. 


No.  4.]  PROPERTIES   OF    VAPORS   OF  ALKALI  METALS.  263 

This  is  of  the  order  of  magnitude  that  would  be  expected.  The  only 
other  determination  made  of  the  vapor  pressure  of  potassium  is  one  by 
Keyes1  from  theoretical  considerations  for  400°  which  he  gives  as  1 .4  mm. 

This  problem  of  conductivity  in  alkali  vapors  is  by  no  means  solved. 
One  very  important  feature  which  should  be  investigated  is  the  effect 
of  ultraviolet  light.  Does  ultraviolet  light  ionize  the  vapor?  And  is 
there  ionization  from  the  electrons  given  off  from  the  metal?  From  the 
data  obtained  some  prediction  can  be  made  on  this  last  point.  Taking 
the  energy  necessary  to  produce  an  ion  to  be  1.58  X  io~n  ergs  we  can 
compute  the  velocity  that  an  electron  should  have  to  produce  ions  by 
collision. 

W  =  y2mv*, 

2.W        2  X  1.58  X  io-n 
VZ       -HT  8.7  X  io-*8         =3.63 

v   =  1.9  X  io8  cm.  per  second. 

If  we  assume  that  the  velocity  of  the  electrons  in  the  photo-electric 
effect  varies  inversely  as  the  wave-length,  we  have 

Xi 

v*  =  v  i  —  . 

A2 

Taking  vi  =  6.21  X  io7  for  Xi  =  4,200  and  \z  =  2,000,  which  is  about  the 
shortest  wave-length  which  can  be  obtained  with  a  quartz  spectrometer, 
we  find 

„  4200 
Vf.  =  6.21  X  io7  - 

2000 

=  1.304  X  io8. 

This  is  less  than  the  value  1.9  X  io8  computed  above.  But  it  is  of 
the  same  order  of  magnitude  and  if  the  minimum  energy  to  produce  an 
ion  is  less  than  1.58  X  io~u  ergs,  it  is  entirely  possible  for  the  electrons 
set  free  from  potassium  by  the  action  of  the  short  wave-lengths  of 
ultraviolet  light  to  produce  ionization  by  collision. 

In  some  other  work  carried  on  by  the  author  a  potential  of  5.85  volts 
was  obtained  from  potassium  illuminated  by  X  2,100.  This  gives  a 
velocity  of  1.445  X  io8  cm.  per  second  which  is  some  nearer  the  critical 
velocity  to  produce  ionization. 

These  values  would  indicate  that  it  would  be  well  worth  while  to  inves- 
tigate this  point. 

i  Jour.  Am.  Chem.  Soc.,  XXXIV.,  p.  779- 


264  S.  HERBERT  ANDERSON.  [VOL.  XXXV. 

SUMMARY. 

1.  This  investigation  has  shown  that  when  potassium  vapor  alone  is 
between  the  electrodes  of  a  tube  there  is  no  conductivity  of  the  usual 
type  at  25°  and  50°;  at  100°  with  a  potential  of  700  volts  there  is  a  current 
arising  from  ionization  by  the  electric  field.     Hence  there  is  nothing  of  the 
character  of  a  spontaneous  ionization. 

2.  When  potassium  was  present  in  the  tube  but  not  in  contact  with  the 
electrodes  there  is  no  conductivity  of  the  usual  type  at  25°  and  50°. 
At  100°  there  is  a  current  due  to  particles  given  off  from  the  potassium. 

3.  In  a  tube  with  two  similar  electrodes  exhausted  to  the  best  degree 
possible  there  is  a  current  of  the  order  io~13  amperes  in  a  direction 
opposite  to  the  electric  field,  which  increases  with  the  field.     This  phe- 
nomenon is  effected  by  light  and  is  decreased  by  the  presence  of  potassium 
vapor. 

4.  The  conductivity  in  potassium  vapor  when  one  electrode  is  potas- 
sium has  been  measured  for  temperatures  up  to  150°. 

5.  The  conductivity  in  caesium  vapor  when  one  electrode  is  caesium 
has  been  measured  for  temperatures  up  to  100°. 

6.  Woodrow's  observations  on  the  emission  of  positive  particles  from 
alkali  metals  have  been  confirmed  and  for  temperatures  above  50°  found 
to  be  large  compared  to  the  electron  current. 

7.  The  ratio  between  the  number  of  electrons  given  off  per  second 
and  the  number  of  atoms  present  has  been  found  for  a  given  source  of 

Hghttobe  5.88  i  !(>'»•  t    - 

8.  At  150°  light  has  practically  no  effect  on  the  emission  of  electrons 
from  potassium. 

9.  By  comparing  the  currents  for  different  temperatures  in  tube  No.  2, 
with  potassium  electrode,  it  is  found  that  the  greatest  relative  effect  of 
light  on  the  emission  of  electrons  is  at  25°. 

10.  The  maximum  vapor  pressure  possible  for  potassium  at  25°  has 
been  found  to  be  0.0587  mm. 

The  author  wishes  to  express  his  indebtedness  to  Professor  A.  P. 
Carman  and  the  department  of  physics  for  the  facilities  for  this  investiga- 
tion, and  to  Professor  Jakob  Kunz  who  suggested  the  problem  and  has 
given  many  valuable  suggestions. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
May,  1912. 


THE  MAGNETIZATION  OF  HEUSLER  ALLOYS  AS  A  FUNCTION 

OF  THE  TEMPERATURE  AND  CALCULATION  OF 

THE  INTRINSIC  MAGNETIC  FIELD 

BY  PERCY  WILCOX  GUMAER 


(Reprinted  from  the  PHYSICAL  REVIEW,  Vol.  XXXV..  No.  4,  Oct..  1912.1 


THE  MAGNETIZATION  OF  HEUSLER  ALLOYS  AS  A  FUNCTION 

OF  THE  TEMPERATURE  AND  CALCULATION  OF 

THE   INTRINSIC    MAGNETIC    FIELD. 

BY  PERCY  WILCOX  GUMAER. 

THE  magnetic  alloys  of  manganese  are  composed  of  metals  which 
ordinarily  are  non-magnetic.  Manganese  itself  is  not  only  non- 
magnetic, but  a  small  per  cent  of  it  will  reduce  the  magnetic  properties 
of  iron.  It  is  probable  that  the  explanation  of  these  magnetic  alloys 
will  add  considerable  to  our  understanding  of  the  ultimate  nature  of 
magnetism. 

Recent  developments  in  the  electron  theory  of  magnetism  have  opened 
up  a  means  of  studying  the  molecular  structure  of  the  alloys. 

The  present  investigation  was  undertaken  with  two  objects  in  view, 
first:  to  study  the  effect  of  temperature  upon  the  saturation  value  of 
the  intensity  of  magnetization.  Then,  to  determine,  if  possible,  from 
the  data  obtained,  the  structure  of  the  molecular  magnets. 

METHOD. 

To  determine  the  saturation  value  of  the  intensity  of  magnetization 
the  method  used  by  Weiss1  and  Stifler2  was  chosen.  A  ballistic  galva- 
nometer was  connected  in  series  with  a  helix  placed  in  a  strong  magnetic 
field.  An  ellipsoid  of  the  alloy  to  be  tested  was  placed  in  the  center  of 
this  helix  and  the  deflection  of  the  galvanometer  was  observed  as  the 
ellipsoid  was,  quickly,  pushed  out.  The  deflection  of  the  galvanometer 
was  then  compared  to  that  obtained  from  the  current  induced  in  the 
secondary  of  a  standard  helix  which  was  included  in  the  circuit.  The 
intensity  of  magnetization  I  can  be  determined  from  the  relation : 

''  -  »* 

where  k  =  a  constant  depending  upon  the  dimensions  of  the  helix  and 

of  the  standard  helix. 
v  =  the  volume  of  the  ellipsoid. 
i  =  current  in  the  primary  of  the  standard  helix. 
df  =  deflection  due  to  induced  current  in  the  standard  helix. 
d  =  deflection  when  ellipsoid  is  removed  from  the  helix. 

1  Archives  des  Sciences,  ser.  4,  29,  pp.  204  (1910). 
*PHYS.  REV.,  Vol.  33,  p.  268  (1911). 


No.  4.  J  THE  MAGNETIZATION   OF  HEUSLER  ALLOYS.  289 

The  ellipsoid  and  helix  were  surrounded  by  a  coil  of  German  silver 
wire,  by  means  of  which  the  desired  temperature  was  obtained.  To 
measure  the  temperature  of  the  ellipsoid  inside  the  helix  a  copper-con- 
stantan  thermo-couple  was  used.  The  hot  junction  was  placed  in  a 
hard  glass  tube  3  mm.  in  diameter  and  26  cm.  long.  Inside  the  tube  the 
wires  were  separated  by  mica  strips,  outside  by  1/16  rubber  tubing. 

The  thermo-couple  was  calibrated  by  observing  the  E.M.F.  of  the 
couple  when  the  hot  junction  was  at  a  known  temperature.  The  tem- 
perature of  steam  and  the  freezing  points  of  metals  were  used  for  the 
calibration,  as  follows:  Zn  419.4°  C.,  Cd  321.0°  C.,  Sn  231.9°  C.,  steam 
1 00°  C.  Using  the  method  of  least  squares  the  constants  of  the  equation 
E  =  at  +  bt2  +  ct*  were  determined  and  the  equation  becomes 

E  =  3.747*  -f-  .00375/2  +  .00000164^. 

The  galvanometer  used  was  a  Leeds  &  Northrup  silver  suspension 
instrument.  It  had  a  resistance  of  25.6  ohms,  a  ballistic  sensibility  of 
31.8  mm.  per  micro-coulomb  on  open  circuit,  with  a  scale  distance  of  50 
cm.,  and  a  period  of  11.2  seconds  on  open  circuit.  At  a  scale  distance 
of  6  meters  and  the  deflection  could  be  read  to  0.5  mm. 

The  ellipsoid  was  inserted  directly  into  the  tube  forming  the  core  of  the 
helix.  It  was  moved  along  by  pushing  with  a  small  glass  rod  in  one 
end  and  with  the  tube  containing  the  thermo-couple  in  the  other  end. 
By  this  method  the  diameter  of  the  helix  could  be  decreased  by  half, 
which  increased  the  sensitiveness  considerably. 

The  induction  helix  was  wound  upon  a  thin-walled  glass  tube  45  cm. 
long  and  0.5  cm.  outside  diameter.  Three  layers  of  number  36  silk- 
covered  copper  wire  were  used.  The  layers  were  separated  by  mica, 
and  each  layer  was  covered  with  a  mixture  of  water  glass  and  calcined 
magnesia.  This  mixture  became  very  hard  when  dry  and  held  the  wires 
firmly  in  place  even  at  high  temperatures. 

A  hard  glass  tube  long  enough  to  reach  to  the  end  of  the  bore  in  the 
magnet  was  slipped  over  the  helix  coil.  Thus  the  possibility  of  leakage 
from  the  heating  circuit  to  the  helix  coil  or  lead-in  wires  was  avoided. 
The  heating  coil  consisted  of  one  layer  of  320  turns  of  number  16  German 
silver  black  enameled  wire.  The  winding  was  done  from  the  middle 
towards  the  ends  so  that  the  two  halves  were  wound  in  opposite  directions 
and  opposed  each  other  magnetically.  As  in  the  induction  helix,  a 
mixture  of  water  glass  and  magnesia  was  used  to  hold  the  wires  firmly 
in  place.  Since  the  length  of  the  coil  was  30  cm.  the  temperature  gradient 
in  the  center  was  very  small. 

The  induction  helix  and  heating  coil  were  enclosed  in  a  glass  tube  small 


290 


PERCY   WILCOX   GUMAER. 


[VOL.  XXXV. 


enough  to  slide  into  the  bore  of  the  magnet.  This  tube  was  filled  with 
calcined  magnesia.  Further  heat  insulation  between  the  pole  pieces  was 
obtained  by  enclosing  that  part  of  the  furnace  in  a  fire  clay  cylinder  filled 
with  shredded  asbestos. 

The  magnetic  field  was  obtained  from  a  large  DuBois  electromagnet. 
A  hole  drilled  through  the  core  and  pole  pieces  enabled  the  ellipsoid 
to  be  inserted  into  the  helix.  For  the  air  gap  used  (6.2  cm.)  the  strength 
of  the  magnetic  field  in  the  center  of  the  gap  was  calibrated  in  terms  of 
the  current  in  the  coils.  A  magnetic  balance  was  used  to  measure  the 
strength  of  the  field. 

DESCRIPTION  OF  SPECIMENS. 

The  alloys  were  prepared  by  melting  in  a  new  graphite  crucible  heated 
in  a  gas  furnace.  The  manganese  and  copper  were  put  in  first,  and 
when  they  were  thoroughly  fused  the  aluminum  was  added.  To  insure 
a  uniform  mixture,  the  molten  alloy  was  stirred  with  a  graphite  rod, 
and  then  quickly  poured  into  vertical  moulds.  Care  was  taken  to  pour 
in  a  continuous  stream  so  that  the  oxide  formed  on  the  surface  would  not 
injure  the  casting. 

The  ellipsoids  were  obtained  by  grinding  the  castings  with  a  properly 
shaped  alundum  wheel  in  a  Universal  Grinder.  A  projection  of  the 
shadow  of  the  ellipsoids  showed  the  cross-section  to  be  fairly  accurate. 

The  dimensions  and  composition  of  the  two  ellipsoids  are  given  as 
follows : 


Ellipsoid  No.  i. 

Ellipsoid  No.  a. 

Length  

1.686  cm. 

1.680  cm. 

Mean  diameter  

0.393  cm. 

0.399  cm. 

Volume 

0.1364  cu.  cm. 

0.1401  cu.  cm. 

Mass  

0.9487  gm. 

1.0028  gm. 

Density  

6.96 

7.15 

Copper                  

62.9  per  cent. 

61.95  per  cent. 

M  anganese 

18.5  per  cent. 

21.9    per  cent. 

Aluminum  

15.1  per  cent. 

15.9    per  cent. 

Undetermined  

3.5  per  cent. 

0.25  per  cent. 

PROCEDURE  IN  TAKING  READINGS. 

After  the  heating  current  had  been  on  for  a  time,  sufficient  to  estab- 
lish temperature  equilibrium,  the  ellipsoid  was  inserted  into  the  core 
of  the  helix.  It  was  moved  along  by  pushing  with  the  tube  containing 
the  thermo-couple  from  one  end  and  with  a  glass  rod  from  the  other 
end.  A  mark  on  the  glass  rod  indicated  when  the  ellipsoid  was  in  the 


No.  4.] 


THE   MAGNETIZATION   OF   HEUSLER  ALLOYS. 


29I 


center  of  the  helix.  When  the  temperature  had  ceased  to  increase  the 
reading  of  the  thermo-couple  was  taken,  the  magnetic  field  was  thrown 
on  and  the  deflection  of  the  galvanometer  was  observed  as  the  ellipsoid 
was  quickly  pushed  out  of  the  helix.  A  rapid  movement  of  the  ellipsoid 
was  obtained  by  striking  the  end  of  the  glass  rod  with  a  small  piece  of  wood. 

The  ellipsoid  was  now  replaced  in  position,  allowed  to  regain  its 
former  temperature  and  the  reading  repeated.  As  a  rule  three  readings 
were  taken  for  each  field  strength  and  the  intensity  of  magnetization  was 
calculated  from  a  mean  of  the  three  deflections. 

At  lower  temperatures  the  deflections  agreed  to  within  I  per  cent,  but 
in  the  neighborhood  of  the  transformation  temperature  the  agreement 
was  not  as  close.  For  some  of  the  readings  taken  above  300°  the  maxi- 
mum deflection  was  I  cm.  at  a  scale  distance  of  6  meters.  The  accuracy 
in  this  case  was  probably  about  10  per  cent. 

After  each  set  of  readings  the  galvanometer  was  calibrated  by  means 
of  the  standard  helix.  The  current  in  the  primary  of  the  helix  was  read 
by  a  Weston  milli-ammeter, 
which  had  been  calibrated  by 
comparison  with  a  standard  in- 
strument. The  ratio  i'ld'  varied 
slightly  as  the  temperature  in- 
creased, due  to  the  increased 
resistance  of  the  helix  coil  at 
higher  temperatures.  As  the 
heating  coil  was  wound  non- 
magnetically,  it  was  not  neces- 
sary to  make  any  correction  for 
it. 

Thermo-couple  readings  were 
taken  just  before  the  ellipsoid 
was  pushed  out  of  the  helix. 
As  the  end  of  the  tube  contain- 
ing the  thermo-couple  was  left  Fi  ^ 
open,  and  as  the  couple  was 

within  a  millimeter  of  the  end  of  the  ellipsoid  when  readings  were  taken, 
it  is  quite  probable  that  the  temperature  measured  corresponded  very 
accurately  to  the  actual  temperature  of  the  ellipsoid. 

RESULTS. 

The  first  set  of  data  obtained  is  apparently  of  little  theoretical  value. 
The  curves  (Fig.  i)  showing  the  specific  intensity  of  magnetism  a  as  a 


25 


IS 


Tempera 


50 


ure 


100 


\ 


'"  ^ 


00 


\ 


250 


292 


PERCY   WIJjCOX  GUMAER. 


[VOL.  XXXV. 


function  of  the  temperature  are  quite  irregular,  having  a  maximum  at 
140°.  Although  it  is  possible  that  the  irregularity  of  these  curves  is  due 
to  a  defect  in  the  apparatus,  it  is  more  probable  that  it  is  due  to  the 
unstable  conditions  of  the  alloys.  The  data  were  obtained  with  the 
alloys  in  the  condition  as  cast  and  without  previous  heat  treatment. 


2.0 


15 


25- 


2.0 


15 


Tempe  -At-ure 
50      IM 


ISO 


90        250 


50 


100 


>° 
150 


2io      250 


Fig.  2. 
Ellipsoid  No.  1. 


Fig.  3. 
Ellipsoid  No.  2. 


A  new  helix  coil  was  now  built  and  a  series  of  readings  taken  at  320° 
indicated  that  the  substance  had  become  paramagnetic.  Beginning  at 
room  temperature,  the  whole  set  of  data  was  repeated  and  very  regular 
curves  were  obtained,  as  shown  in  Figs,  a  and  3.  These  curves,  showing 
<r,  the  specific  intensity  of  magnetization,  as  a  function  of  the  tempera- 
ture, are  similar  to  the  ones  obtained  for  iron,  nickel  and  cobalt,  although 
they  are  much  flatter  at  lower  temperatures.  It  is  seen  from  the  curves 
that  the  temperature  of  transformation  is  in  the  neighborhood  of  310°. 
A  theoretical  discussion  of  these  curves  will  be  given  in  a  later  paragraph. 

As  the  values  of  cr  at  room  temperature  were  found  to  be  about  half 
of  what  should  be  expected  from  the  theoretical  calculations,  an  attempt 
was  made  to  increase  the  magnetic  intensity  by  chilling  from  a  tempera- 
ture near  the  melting  point  of  the  alloy.  To  do  this  the  ellipsoids  were 
inserted  in  a  quartz  tube  together  with  a  platinum  platinum-rhodium 


No.  4.] 


THE   MAGNETIZATION  OF  HEUSLER  ALLOYS. 


293 


thermo-couple,  and  heated  in  an  electric  furnace  to  895°  C.  They  were 
kept  at  the  temperature  for  10  minutes  and  then  chilled  by  plunging 
the  quartz  tube  into  cold  water. 

The  value  of  the  intensity  of  magnetization  was  found  to  have  been 
increased  considerably  by  the  chilling.  Values  of  <r  were  obtained,  as 
before,  for  different  values  of 
temperature  below  the  transfor- 
mation point.  The  curves  are 
shown  in  Fig.  4. 

In  order  to  be  sure  of  the  re- 
sults the  chilling  was  repeated 
for  ellipsoid  No.  I  and  similar 
values  were  obtained. 

The  following  table  shows  a 
typical  set  of  readings  taken  at 
290°  C.  The  value  of  a  at  each 
field  strength  was  obtained  from 
the  mean  of  three  galvanometer 
deflections.  The  temperature 
was  obtained  from  the  mean  of 
the  thermo-couple  readings.  p. 

These  were  not  allowed  to  vary 
more  than  20  micro-volts,  which  corresponds  to  o.46. 


SO 


SO 


mv 

d 

Mean,,- 

<r 

/ 

LI 

fm 

ft 

H 

13,670 

27.5     ! 

13,680 

27.3     i 

27.4     i 

15.9 

114.0 

85 

2.0         : 

930 

845 

13,675 

27.5 

13,670 

27.S 

13,680 

27.7 

27.7     ' 

16.1 

115.3 

86 

3.0 

1,395 

1,309 

13,670 

27.7 

13,675 

29.0 

13,665 

28.8 

29.0 

i6.a 

120.5 

90 

4.0 

1,860 

1,750 

13,665 

29.2 

M 

13,670 

29.0 

*  .'  1 

13,670 

28.7 

23.9 

16.75 

120.0 

90       ; 

5.0 

2,335 

2,245 

13,675 

29.0 

13,670 

29.0 

13,670 

28.8 

28.9 

16.75 

120.0 

90 

6.0 

2,730 

2,640 

13,665 

28.9 

294  PERCY  WILCOX  GUMAER.  [VOL.  XXXV. 

TYPICAL  SET  OF  DATA.    TAKEN  AT  290.9°. 

Ellipsoid  No.  2. 

I  =  4.157^,         a  =  0.580^,         L  =  0.749. 
d  =  deflection  of  the  galvanometer, 
mv  =  reading  of  thermo-couple  in  microvolts, 
Im  =  current  through  the  magnet, 
Ho  =  external  field, 

H  =  field  inside  the  ellipsoid  =  HQ  —LI, 
I  =  intensity  of  magnetization, 
a  =  specific  intensity  of  magnetization. 
Mean  value  of  thermo-couple  readings  =  13,670  m.v. 
Corresponding  temperature  =  290.9°. 
Deflection  due  to  standard  helix  =  70.3. 
Current  in  primary  of  standard  helix  =  0.672  ampere. 

MOLECULAR  THEORY  OF  MAGNETISM. 

The  present  theory  of  magnetism,  as  developed  by  Curie,1  Weiss,2 
Langevin3  and  Kunz,4  accounts  for  the  various  phenomena  by  assuming 
that  a  magnetic  substance  is  made  of  small  elementary  magnets. 

In  a  non-magnetic  state  these  elementary  magnets  are  distributed  with 
their  axes  pointing  equally  in  all  directions.  Under  the  influence  of  a 
resultant  magnetic  field  H,  each  elementary  magnet  is  acted  upon  by  a 
turning  force  MH  sin  a,  where  M  is  the  moment  of  the  elementary 
magnet  and  a  is  the  angle  between  H  and  the  axis  of  the  magnet.  The 
tendency  of  this  couple  is  to  cause  the  magnets  to  turn  with  their  axes 
toward  the  direction  of  the  existing  field.  The  amount  of  this  rotation 
depends  upon  the  strength  of  the  field  and  upon  the  temperature  of  the 
substance. 

If  there  were  no  thermal  agitation  of  the  molecules  all  the  elementary 
magnets  would  revolve  until  their  axes  coincided  with  the  direction  of  the 
existing  field.  This  condition  is  obtained  at  absolute  zero. 

At  other  temperatures  than  absolute  zero  the  magnetic  energy  of  the 
molecules  tending  to  arrange  the  molecules  in  the  direction  of  the  magnetic 
field  is  opposed  by  the  thermal  energy.  The  molecules  are  continually 
being  deflected  by  their  mutual  collisions,  and  the  resultant  condition  of 
equilibrium  depends  upon  the  ratio  of  the  thermal  energy  to  the  magnetic 
energy. 


1  Archives  des  Sciences,  ser,  4,  31,  p.  5-19 

2  Journal  de  Physique,  36,  p.  661-690  (1907). 

8  Annales  de  Chemie  et  de  Physique,  Ser.  5,  8,  p.  70-127  (1905). 
4  PHYS.  REV.,  30,  p.  359-370  (1910). 


No.  4.]  THE   MAGNETIZATION   OF  HEUSLER  ALLOYS.  2Q5 

Consider  a  sphere  of  unit  radius  within  which  are  a  large  number  of 
magnetic  molecules.  When  there  is  no  magnetic  field  acting,  the  magnets 
are  distributed  with  their  axes  pointing  equally 
in  all  directions.  Imagine  all  these  magnets 
concentrated  with  their  centers  at  o.  Under 
the  action  of  a  magnetic  field  the  magnets 
will  be  caused  to  rotate  about  o,  and  the  ten- 
dency will  be  to  place  their  axes  in  line  with 
the  magnetic  field.  The  magnets  will  no 
longer  have  their  axes  pointing  uniformly  in 
all  directions,  but  the  magnetic  density  will  be  F. 

greatest  in  the  direction  of  H.     Let  us  define 

magnetic  density  as  the  number  of  magnetic  axes  per  unit  solid  angle 
or  dn/du.  For  abbreviation  put  p  —  dnjd^. 

Let  p  be  the  magnetic  density  at  any  angle  a  with  the  field  H.  Then 
at  angle  a  +  da  the  magnetic  density  will  be  p  -f  (dp/da)da.  The 
change  of  magnetic  density  in  moving  through  angle  da  is  therefore 

dp 
dada' 

This  change  of  density  depends  upon  the  density  p  at  a.  It  is  also 
proportional  to  a  resultant  turning  force  or  couple. 

If  we  assume  that  the  molecules  of  iron,  or  other  ferro-magnetic 
substance,  when  in  a  non-magnetic  state  are  as  free  to  move  relatively 
to  each  other  as  the  molecules  of  a  gas,  then  the  thermal  energy  can  be 
deduced  from  the  laws  of  thermo-dynamics.  Since  a  rotation  of  the 
elementary  magnet  about  its  own  axis  has  no  effect  upon  its  magnetic 
energy,  there  remain  but  two  degrees  of  rotation.  Hence,  for  the  molecu- 
lar magnets,  the  kinetic  energy  of  heat  is  equal  to  RT,  where  R  is  the 
universal  gas  constant  and  T  is  the  absolute  temperature. 

In  dynamics  work/angle  =  a  couple,  hence  RT/da  =  a  couple  due  to 
the  thermal  energy  of  the  molecules.  The  magnetic  couple  acting  upon 
the  elementary  magnets  is  MH  sin  a. 

The  change  of  magnetic  density  varies  directly  as  the  magnetic  couple 
and  inversely  as  the  couple  due  to  the  heat  energy;  that  is,  the  greater 
the  magnetic  couple,  the  greater  will  be  the  change  of  magnetic  density 
as  we  pass  from  a  to  a  -\-  da,  and  the  greater  the  thermal  energy,  the 
smaller  will  be  the  change  of  density.  Hence  we  can  put 

dp  MH  sin  a         MH  sin  a  •  da 


/      ,dp      \ 

~  \  P  +  ~r  da  i  =  ~ 

\          da       / 


da 


296  PERCY   WI'LCOX  GUMAER.  [VOL.  XXXV. 

Then 

_  dp  =     MH  . 

and 

dp      MH  . 

P 
Integrating 

MH 
log  p  =  -j^r  cos  a  -  log  K\ 

whence, 


or 

^7*»  -^-H" 

—  -  Kexr 
,     —  j.\.c 

aw 
But 

do)  =  2ir  sin 
hence 

ATg  (T\ 

</w  =  .KVflF00'"  27T  sin  ada. 

Intensity  of  magnetization  may  be  defined  as  the  product  of  the 
number  of  molecular  magnets  per  unit  voluihe  and  the  moment  of  the 
magnets  in  the  direction  of  the  resultant  magnetic  field.  The  intensity 
is  a  maximum  when  there  is  no  thermal  agitation,  so  that  the  molecular 
magnets  are  all  directed  along  the  field.  This  condition  obtains  only 
at  absolute  zero. 

At  other  temperatures  the  intensity  due  to  the  magnets  whose  axes 
make  an  angle  a  with  H  is 

dl  —  M  cos  ctdn, 

where  M  is  the  moment  of  the  molecular  magnets,  and  /  is  the  intensity 
of  magnetization. 

Substituting  the  value  of  dn  from  eq.  (i),  we  have 

MH 

dl  =  M  cos  KeRT  co ' a  2*r  sin  ada', 
and  integrating  between  limits  o  and  TT 

fir  MH 

Mcos  aKeRT  ™*a 2ir  sin  ada. 
, 
Now  let 

MH  •      * 

-&~  =  tf,     cos  a  =  x,      —  sin  ada  =  dx\ 

J\.l 

then, 


NO.  4-1  THE   MAGNETIZATION  OF  HEUSLER  ALLOYS.  £97 


=  2irMK  I      xe**dx. 
+l 

But 


hence 

(a) 

To  evaluate  K,  integrate  equation  (i)  : 

n  =  2irK  I    eaC06asmada 

4*K  . 

= smh  a ; 

d 

Whence 

na 


K  = 


4?r  sinh  a 
Substituting  the  value  of  K  in  equation  (2),  we  have 


t ,.       na       I  cosh  a       sinh  a  \ 

2.2irM        .  ,      I  -  —  -  -       -  1 

4T  sinh  a  \      a  a2     / 

__    /cosh  a      i\ 
Mn  I    .  ;      —  -  J . 

\  sinh  a      a  7 


But  Mw  =  /„;  hence, 

cosh  a 


where 

M  H 

(4) 


Equations  (3)  and  (4)  give  us  an  expression  for  the  intensity  of  mag- 
netization as  a  function  of  the  temperature. 

So  far  we  have  considered  only  the  arrangement  of  the  elementary 
magnets  due  to  the  action  of  an  external  field.  Each  magnet,  however, 
has  an  effect  upon  the  surrounding  magnets  and  the  result  according  to 
the  Weiss  theory  is  a  uniform  field,  proportional  to  the  intensity  of 
magnetization,  7,  and  acting  in  the  same  direction  as  /.  This  molecular 
magnetic  field  accounts  for  the  great  magnetic  intensity  of  iron  and 


298  PERCY   WILCOX   GUMAER.  [VOL.  XXXV. 

other  ferro-magnetic  substances  in  the  same  way  as  an  internal  pressure 
added  to  the  external  pressure  accounts  for  the  great  density  of  liquids. 
The  sudden  increase  of  density  when  a  vapor  liquefies  is  due  to  the  fact 
that  an  enormous  internal  pressure  is  suddenly  made  effective  in  addition 
to  the  external  pressure.  Ferro-magnetic  substances  at  high  tempera- 
tures are  but  slightly  magnetic.  As  the  temperature  is  slowly  decreased 
a  point  is  reached  at  which  the  substances  suddenly  become  very  mag- 
netic. This  indicates  that  a  strong  molecular  field  has  become  operative. 
If  Hm  represents  the  molecular  field  and  /  the  intensity  of  magnetization 
then  Hm  =  A  I  where  A1  is  a  proportionality  factor. 

The  resultant  magnetic  field  within  the  substance  is,  consequently,  the 
sum  of  the  external  field,  He  and  the  molecular  field  Hmj  or,  H  =  He  +  Hm. 

From  equation  (4) 


aR 
whence 


The  large  magnetic  intensity  of  ferro-magnetic  substances  at  ordinary 
temperatures  indicates  that  the  molecular  field  must  be  very  strong  in 
comparison  with  the  external  field.  This  condition  holds  up  to  the 
temperature  at  which  the  substance  ceases  to  be  ferro-magnetic.  Let  6 
be  that  temperature,  then  for  T  =  0,  we  can  neglect  He  in  comparison  to 
Hm  and  equation  (5)  becomes 


From  equation  (3) 

/cosh  a       i\ 

m  \sinh  a       a/' 

/  cosh  a      I  \ 

The  expression  I  -r*-  --  -  I  can  be  expanded  into  the  convergent 
\  smh  a      a  I 


seres 

-a   _   — 


3          90  45*42 


For  very  small  values  of  a  it  is  sufficient  to  consider  only  the  first  term 
of  the  series,  and  equation  (3)  becomes 


1  In  order  to  avoid  ambiguity  later  the  symbol  A  is  chosen  in  preference  to  N,  the  symbol 
used  by  Weiss,  Kunz  and  others. 


No.  4.3  THE  MAGNETIZATION  OF  HEUSLER  ALLOYS.  2  99 

For  T  =  0  equation  (5)  may  be  written 

-^•'     - 

Dividing  equation  (5)  by  (7),  we  have 

M(He  +  AT) 
T  aR 


_ 

B   '          MAI 

3R 
But 


hence 

Solving  for  A  ,  we  have 


-      '    4-  T 
8  ~Tl  ' 


He     6 


Knowing  A,  we  can  calculate  Hm,  the  strength  of  the  molecular  field, 
since  Hm  =  AI. 

We  can  also  calculate  M,  the  moment  of  the  elementary  magnet, 
for  from  equation  (7)  we  have 

.MAI,, 

3*    ' 
or 

• 


«- 


DISCUSSION  OF  RESULTS. 

The  curves  (2)  and  (3),  showing  a  as  a  function  of  the  temperature 
indicate  that  the  temperatures  at  which  the  alloys  cease  to  be  ferro- 
magnetic is  in  the  neighborhood  of  310°  C. 

Knowing  6  it  is  possible  to  express  T  as  a  function  of  the  parameter  a. 
Then  by  comparing  the  graph  obtained  with  the  experimental  curve 
near  the  transformation  point,  we  can  calculate  a  value  for  Im,  the 
intensity  of  magnetization  at  absolute  zero. 

Equation  (50)  can  be  written  in  the  form 


=      - 

=  MA' 


Dividing  through  by  Im,  we  have 


300 

But  from  equation  (7) 

hence 

and 


PERCY   WILCOX   GUMAER. 

I  R 


[VOL.  XXXV. 


rw     MAim 

MAIm  =  2 
I        i 


aT. 


_30j[  _  30 /cosh  a  _  i\ 
a  Im       a  \sinh  a      a  I 


(12) 


Putting  0  =  310°  -f-  273°  =  583° 
obtain  the  following  values  : 


and  evaluating  equation   (12),  we 


a 

cosh  a 

sinh  a 

0-   cosh  a   Z. 

T 

t 

^ 

ffm   sinh  a   a 

0.3 

3.4328 

0.0995 

580 

307 

7.0 

0.4 

2.6317 

0.1317 

577 

304 

9.8 

0.5 

2.1639 

0.1639 

574 

301 

12.2 

0.6 

1.8619 

0.1952 

569 

296 

14.5 

0.8 

1.5059 

0.2559 

560 

287 

19.1 

1.0 

1.3131 

0.3131 

548 

275  . 

23.3 

1.2 

1J995 

0.3662 

534 

261 

27.3 

1.6 

1.0849 

0.4599 

503 

230 

34.3 

2.0 

1.0373 

0.5373 

470 

197 

39.9 

.  3.0 

1.0049 

0.6716 

392 

119 

50.0 

4.0 

1.0007 

0.7507 

328 

55 

55.9 

5.0 

1.0000 

0.8000 

280 

7 

59.6 

Since 


cosh  a      i' 
sinh  a      a 

where  am  is  the  value  of  0-  at  absolute  zero. 

In  the  following  table  the  experimental  values  of  <r  are  compared  with 
the  calculated  values  of  <7/<7m  for  values  of  t  above  250°. 


t 

o-  Observed. 

<r'<Tm  Calculated. 

Value  of  <rm. 

297.7 

12.9 

.184 

70.1 

297.7 

13.5 

.184 

73.4 

290.9 

17.6 

.234 

75.5 

290.9 

16.8 

.234 

71.8 

258.9 

28.5 

.373 

76.6 

74.5  mean 

No.  4-1 


THE  MAGNETIZATION   OF  HEUSLER  ALLOYS. 


301 


60 


It  is  evident  that  if  we  divide  the  observed  values  of  <7  by  the  calculated 
values  of  <r/ffm  we  can  determine  the  value  of  *,».  Taking  the  mean 
of  several  values,  we  get  o-«  =•  74.5.  If  we  now  multiply  the  values  of 

7-r -  by  74.5,  we  obtain  corresponding  values  for  <r  and  /.     Using 

sinn  CL      d 

these  values  we  can  plot  a  theoretical  curve  for  a  and  the  temperature. 
Such  a  curve  is  shown  in  Fig.  6. 

It  will  be  noticed  that  the  experimental  values  of  <r  as  given  by  the 
dotted  lines  agree  with  the  theoretical  values  for  high  temperatures,  but 
at  low  temperatures  the  experi- 
mental curve  bends  away  from 
the  other.  The  same  phenome- 
non is  observed  in  iron,  nickel 
and  cobalt,  but  to  a  lesser  de- 
gree. In  the  case  of  the  mag- 
netic alloys  the  bending  is  less 
(curve  B)  after  the  alloy  has 
been  chilled  from  a  high  temper- 
ature. 

Since  the  internal  or  molecular 
field  becomes  negligible  above  the 
transformation  temperature,  the 
intensity  of  magnetization  be- 
comes proportional  to  the  exter- 
nal field,  and  from  a  knowledge 
of  the  magnetic  properties  of  the 
alloy  in  its  paramagnetic  state 
we  calculate  Hm  the  intrinsic 
molecular  field  and  m  the  moment  of  the  elementary  magnets. 

In  doing  this  we  will  first  calculate  A,  the  proportionality  con- 
stant. 

From  equation  (8)  we  have 

H.     e 

A    =  —=r  ^- 


20 


A-  #1 


Tempe  vrure 
50      190 


2TO 


Fig.  6. 


I   T-  tf 

where  Ht  is  the  external  field  and  /  is  the  intensity  of  magnetization  at 
temperature  T. 

Calculations  of  A  are  given  in  the  following  table  for  various  values  of 
T.  They  give  for  ellipsoid  No.  I  A  =  12^940;  for  ellipsoid  No.  2 
A  =  10,540. 


302 


PERCY   WILCOX   GUMAER. 


[VOL.  XXXV. 


Ellipsoid  No.  1. 


Temp.  =314.5°. 

Temp.  =  320°. 

H. 

/ 

K=I\He 

H. 

/ 

K 

462 

3.93 

.00851 

465 

1.98 

.00427 

924 

7.42 

.00803 

927 

4.02 

.00434 

1,382 

14.4 

.01041 

1,390 

6.23 

.00448 

1,844 

17.9 

.00973 

1,853 

7.56 

.00408 

2,319 

18.2 

.00788 

2,326 

10.25 

.00440 

Mean  .00891 

A  =  14,560 

Mean  .00439 

A  =  13,270 

Temp.  =  327.7°. 

Temp.  =  340°. 

a. 

/ 

K 

He 

/ 

K 

464 

1.31 

.00282 

1,394 

1.79 

.001284 

928 

2.62 

.00282 

2,726 

4.15 

.001521 

1,392 

3.92 

.00282 

3,425 

5.68 

.001658 

1,855 

5.23 

.00282 

3,695 

7.0 

.001894 

2,329 

6.54 

.00281 

Mean  .00282 

A  =  11,700 

Mean  .00159 

A  =  12,230 

Ellipsoid  No.  2. 


Temp.  =  314.5°. 


ff. 

7 

K=HH. 

ffe 

/ 

K 

463 

4.61 

.00996 

463 

2.26 

.00489 

923 

9.66 

.01046 

926 

5.83 

.00630 

1,384 

15.14 

.01094 

1,389 

7.96 

.00573 

1,846 

18.92 

.01026 

1,852 

10.83 

.00584 

2,326 

12.00 

.00518 

Mean  .01040 

A  =  12,460 

Mean  .00559 

A  =  10,430 

Temp.  =  340°. 

Temp.  =  360°. 

ffe 

/ 

K 

H. 

/ 

K 

1,393 

2.74 

.001966 

1,394 

1.904 

.001365 

2,726 

5.77 

.002115 

2,728 

3.38 

.001240 

3,425 

6.74 

.001967 

3,427 

4.23 

.001233 

3,825 

7.37 

.001926 

3,827 

4.02 

.001050 

Mean  .001993 

A  =  9,760 

Mean  .001227 

A  =  9,500 

Temp.  =  320°. 


Ellipsoid  No.  i. 

Ellipsoid  No.  2. 

Temp. 

A 

Temp. 

A 

314.5 
320.0 
327.7 
340.0 

14,560 
13,270 
11,700 
12,230 

314.5 
320.0 

340.0 
360.0 

12,460 
10,430 
9,760 
9,500 

Mean  A  =  12,940 

Mean  A  =  10,540 

No.  4.] 


THE  MAGNETIZATION   OF  HEUSLER  ALLOYS. 


303 


The  calculation  of  the  other  quantities  consists  merely  in  substituting 
in  the  equations  already  obtained.     The  work  is  summarized  as  follows: 


Ellipsoid  No.;x. 

Ellipsoid  No.  a. 

0m, 

74.5 

74.5 

d 

=  density, 

6.96 

7.15 

I. 

=  dffm, 

518 

533 

He      6 

A 

(8) 

12,940 

10,540 

I  T-e  ' 

Hm 

~AI», 

6,700,000 

5,620,000 

M 

3-K1^ 

(9) 

3.55  •  10-*° 

4.23  •  1C 

"  AIm' 

N 

-^ 

(10) 

1.46  •  10» 

1.26  •  1C 

R  =  1.36  •  io~16. 

For  comparison,  the  constants  obtained  for  iron  and  nickel  by  Kunz2 
and  for  cobalt  by  Stifler3  are  given  in  the  following  table : 


/* 

e 

A 

fti 

MX  io-*>. 

A^Xio22. 

Iron  

2,120 

756°  C. 

3,850 

6,560,000 

5.15 

4.12 

Cobalt 

1  435 

1  075 

6  180 

8  870  000 

621 

2  31 

Nickel  

570 

376 

12,700 

6,350,000 

3.65 

1.56 

Alloy  No.  1  . 
Alloy  No.  2  . 

518 
533 

310 
310 

12,940 
10,540 

6,700,000 
5,620,000 

3.55 
4.23 

1.46 
1.26 

If  we  assume  that  there  is  one  atom  of  manganese  in  the  magnetic 
molecule  then  for  alloy  number  one  we  have  the  relation 


wn 

where  mH  =  weight  of  a  hydrogen  atom. 

w  =  55  =  atomic  weight  of  manganese. 
n  =  1.46'  io22  the  number  of  magnetic  molecules  per  cu.  cm. 
d  =  density  of  alloy  X  per  cent,  of  manganese  in  alloy. 
=  6.96-0.185. 

6.96-0.185 


mH  = 


IO22  =  I.60-IQ-24. 


1  R  is  the  universal  gas  constant,  and  the  value  to  be  used  is  that  corresponding  to  one 
molecule. 

2  PHYS.  REV.,  Vol.  30,  p.  259  (1910). 
1  PHYS.  REV.,  Vol.  33,  p.  268  (1911). 


304  PERCY   WILCOX  GUMAER.  [VOL.  XXXV- 

This  value  of  mH  agrees  almost  exactly  with  1 .61  •  IQ-24,  the  value  obtained 
by  Rutherford.  From  alloy  number  two  we  get  mH  =  2.I2-IO"24, 
which  does  not  agree  very  closely. 

If  e  is  the  elementary  charge  of  the  hydrogen  atom  and  an  is  the 
chemical  equivalent  of  hydrogen,  then  e  =  mH/aH.  Using  the  values  of 
mH  obtained  above  we  get  from  alloy  number  one  e  =  i.54-io~20  and 
from  alloy  number  two  e  =  2.04 -io~20. 

We  could  have  obtained,  however,  the  same  values  by  assuming  that 
the  magnetic  molecule  was  composed  of  one  atom  of  manganese  and  one 
atom  of  aluminium,  or  one  atom  of  manganese  and  one  atom  of  copper. 
Since  a  molecule  must  contain  more  than  one  atom,  it  is  quite  probable 
that  the  magnetic  molecule  is  a  composite  molecule  containing  one  atom 
of  mangenese  and  one  atom  either  of  copper  or  of  aluminium.  This 
hypothesis  would  also  account  for  the  increase  in  the  intensity  of  magnet- 
ism after  chilling  from  a  high  temperature,  as  shown  in  Fig.  6.  The 
chilling  prevents  one  of  the  metals  from  crystallizing  out  and  thus 
prevents  a  decrease  in  the  number  of  molecular  magnets. 

The  author  hopes  to  continue  the  investigation  and  to  determine 
definitely  the  number  and  kind  of  atoms  in  the  elementary  magnet,  and 
also  to  study  the  effect  of  the  percentage  of  copper  upon  the  transforma- 
tion temperature.  These  results  will  be  important  in  proving  that  the 
magnetic  properties  are  due  to  the  manganese. 

SUMMARY. 

The  chief  results  of  this  investigation  may  be  summarized  as  follows: 

1.  The    temperature    of    magnetic    transformation    from    the    ferro- 
magnetic to  the  paramagnetic  state  was  established  at  310°  C.  for  the 
alloys  containing  62  per  cent,  copper. 

2.  The  curve  giving  a  as  a  function  of  the  temperature  has  been  shown 
to  agree  with  the  theoretical  curve  above  200°. 

3.  Chilling  from  near  the  melting  point  causes  the  experimental  curve 
to  follow  the  theoretical  curve  to  a  lower  temperature  than  before. 

4.  The  nature  of  the  molecular  field  was  found  to  be  of  the  same 
order  of  magnitude  as  nickel,  all  the  constants  Im,  Hm,  M  and  H,  being 
of  approximately  the  same  value. 

5.  The  results,  while  not  extensive  enough  to  determine  the  number 
and  kind  of  atoms  in  the  elementary  magnet,  are  sufficient  to  show  that 
the  alloys  obey  the  laws  of  ferro-magnetism,  as  derived  by  the  present 
molecular  theory. 

6.  The   fundamental   equation    (i),  on  which  the  present  theory  of 


No.  4.]  THE  MAGNETIZATION  OF  HEUSLER  ALLOYS.  305 

magnetisms  be  said,  has  been  derived  mathematically;  thereby,  making 
the  former  analogy  to  the  gas  theory  unnecessary. 

The  writer  takes  pleasure  in  acknowledging  his  indebtedness  to  Pro- 
fessor Jakob  Kunz  for  his  general  supervision  of  the  work,  and  for  many 
valuable  suggestions. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
April  25,  1912. 


[Reprinted from  SCIENCE,  N.  8.,  Vol.  XXXVL,  No. 
9S7,  Pages  8S7-8S8,  December  IS,  1912] 


A    SIMPLE    DISCHARGE    TUBE    FOR    DEMONSTRATION 
PURPOSES 

AT  the  present  time  when  so  much  interest 
is  centered  on  electric  discharge  phenomena 
in  evacuated  tubes  it  may  not  be  out  of  place 
to  describe  one  of  the  discharge  tubes  that  the 
writer  used  recently  for  class-room  demonstra- 
tion. The  experiment  is  purely  qualitative, 
and  in  principle  contains  nothing  new.  Its 
aim  is  to  present  with  simple  and  easily  con- 
structed apparatus  some  of  the  phenomena 
that  are  usually  given  with  more  elaborate  and 
expensive  outfits.  It  does,  however,  require 
that  the  experimenter  have  access  to,  and  be 
familiar  with,  the  operation  of  an  ordinary 
Geissler  mercury  pump  and  an  induction  coil. 
Aside  from  these  the  things  needed  are  found 
in  almost  any  laboratory  and  require  no  more 
skill  to  make  than  the  blowing  of  a  glass  Tee. 

The  discharge  tube  in  question  is  shown  in 
the  figure.  The  bulb  may  well  be  a  two-  or 
three-liter  florence  flask.  The  part  to  be 
blown  is  MN.  It  supports  the  aluminum  rod 
carrying  at  its  upper  end  the  spherical  or 
oblong  cathode,  C,  of  the  same  metal.  The 
anode,  A.,  is  a  cylinder  of  not  too  light  weight 
aluminum  foil  placed  in  the  neck  of  the  flask 
as  shown.  Connection  to  this  is  made  by  a 
fine  copper  wire  led  out  through  the  wax  joint, 
RW,  at  the  mouth  of  the  flask.  The  exhaust 
tube  should  contain  a  glass  valve  and  ter- 
minate in  a  sort  of  ball  and  socket  joint  (to  be 
sealed  with  wax)  so  that  the  apparatus  may 
be  readily  disconnected  from  the  pump.  The 
charcoal  bulb,  CB,  may  be  dispensed  with 
where  liquid  air  is  not  available.  Liquid  air 


is  not  a  necessity;  its  use,  as  is  well  known,  is 
to  hasten  the  exhaustion.  The  three  joints, 
RW,  may  be  closed  sufficiently  air-tight  by  a 
good  grade  of  red  sealing  wax. 

The  various  steps,  as  the  exhaustion  pro- 
ceeds, may  be  vividly  shown — the  stringy  dis- 
charge, the  Geissler  stage,  the  formation  of 
striae,  the  Faraday  dark  space  followed  by 
Crookes  dark  space,  and  finally  the  formation 
of  cathode  and  X-rays.  The  phosphorescence 
due  to  the  latter  is  strikingly  shown  by  intro- 
ducing into  the  bulb  a  few  cubic  centimeters 
of  willemite  flour  (W  in  the  figure).  This 
should  be  well  dusted  over  the  inner  surface 
of  the  bulb  before  sealing  the  apparatus  to 


8 


the  pump.  A  particularly  beautiful  effect, 
at  the  cathode-ray  stage,  is  to  disconnect  the 
pump  and  then  shake  the  bulb  vigorously  so 
as  to  throw  the  flour  through  space  while  the 
discharge  is  passing. 


I" 

11 

Ill 

Maximum  D.C. 

|| 

11 

J*s 

Available  Was 
1,000  Volts 

Remarks 

2* 

a 

s^-2 

^g 

2.0 

Passed 

1.5 

freely. 
More 
freely. 

480 
440 

Thedischagein 
each  case  was 

Blue  at  cathode. 

.5 

Still  more 

more   volumi- 

freely. 

360 

nous  than  with 

U       «               <i 

the    induction 

.08 
.01 

Same. 
Less 
freely. 

360 
500 

coil. 
Discharge  same 

Willemite  began 
,o  phosphoresce. 
Willemite     a 

.006 

Still  less 

as      induction 
coil. 

beautiful  green. 

freely. 

560 

Less    than    in- 

Weaker. 

duction  coil. 

.005 

Small. 

680 

Much  less  than 

Still  weaker. 

induction  coil. 

.004 

Faint. 



^o  discharge. 

Ceased  to  phos- 

.003 

None. 

phoresce. 

It  may  be  of  interest  to  add  that  the  tube 
works  well  on  direct  current  of  fairly  low 
voltage.  For  that  purpose  ordinary  high 
potential  storage  cells  (of  capacity  one  tenth 
ampere  normal  discharge  rate)  may  be  em- 
ployed. To  guard  against  too  great  a  current 
flowing  through  the  discharge  tube  an  adjust- 
able water  resistance  should  be  included  in 
the  storage-battery  discharge  circuit.  The 
effect  upon  the  ease  with  which  the  storage 
battery  discharge  passes  through  the  tube  may 
be  nicely  shown  by  first  ionizing  the  remain- 
ing gases  in  the  tube  by  means  of  the  high 
potential  induction  coil  discharge,  and  then 
switching  instantly  to  the  storage  cells.  The 
minimum  direct-current  voltage  that  will,  for 


a  given  pressure,  produce  a  discharge  may 
thus  be  obtained.  This  minimum  voltage 
together  with  other  data  and  remarks  are 
given  in  the  accompanying  table. 

CHAS.  T.  KNIPP 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OP  ILLINOIS 


(Reprinted  from  the  PHYSICAL  REVIEW,  Vol.  XXXV.,  No.  6,  Dec.,  1912.] 


DETERMINATION    OF   CAPACITIES    BY    MEANS   OF 
CONJUGATE   FUNCTIONS. 

BY  J.  W.  WOODROW. 

^HIS  paper  is  intended  to  make  use  of  the  properties  of  conjugate 
-*-  functions  for  the  solution  of  a  few  problems.  The  cases  to  be 
considered  are  those  in  which  the  surfaces  of  electrical  conductors  are 
generated  by  the  motion  of  straight  lines  all  parallel  to  a  straight  line 
which  will  be  taken  as  the  axis  of  z.  These  conductors  are  to  be  considered 
sufficiently  long  in  this  direction  so  that  when  charged,  the  z-component 
of  the  electric  force  may  be  neglected.  Then  if  that  portion  of  the  field 
between  two  planes  parallel  to  the  rry-plane  and  unit  distance  apart  be 
considered,  the  potential  and  distribution  of  electricity  become  functions 
of  x  and  y  only.  If  a  relation  can  be  found  between  w  and  z  where 

w  =  u  +  iv    and     z  =  x  -\--iy, 

which  will  transform  straight  lines  in  the  w-p\ane  into  curves  in  the 
2-plane  which  coincide  with  the  lines  of  intersection  between  the  equi- 
potential  surfaces  and  a  plane  perpendicular  to  them,  expressions  for 
the  capacity  of  the  system  and  for  the  surface  distribution  can  be  easily 
found.1 

In  the  following  transformations,  the  equipotential  surfaces  will  be 
given  by  u  equal  to  a  constant  and  the  lines  of  force  by  v  equal  to  a 
constant.  The  charge  e  will  indicate  the  charge  on  unit  length  of  the 
conductor  and  the  capacity  C  will  represent  the  capacity  per  unit  length. 

Consider  first  the  simple  case  of  the  surface  distribution  on  a  very 
long  wire  parallel  to  an  infinite  plane  conductor  at  zero  potential.  It  is 
well  known  that  the  transformation 

w=log-  (i) 

z  —  a 

will  give  the  equipotential  lines  and  lines  of  force  for  the  above  condition. 
The  capacity  as  given  by  this  transformation  will  be  found  in  Webster's 
Electricity  and  Magnetism,  where  it  is  also  shown  that  the  surface  dis- 

1  Electricity  and  Magnetism,  J.  H.  Jeans,  p.  256;  Electricity  and  Magnetism,  A.  G.  Web- 
ster, p.  307. 


435  J-   w-  WOODROW.  [VOL.  XXXV. 

tribution  for  any  transformation  by  means  of  the  complex  variable  is 
given  by 

dw 


dz 
By  differentiating  (i) 

dw      2a[(a2  —  x2  -f-  y2)  +  2ixy] 
~dz  =      (a2  -  x2 
and  hence 


(2) 


dz 


y2) 


(a2  - 


(3) 


Whence 

a  = •  a .  (4) 

2irV(a?  -  x*  +  y2)2  +  4jcy 

Now  a  more  convenient  form  is  obtained  by  changing  to  polar  coordi- 
nates with  the  origin  at  the  center  of  the  wire.  If  r  is  the  radius  of  the 
wire  and  d  is  the  distance  of  its  center  from  the  infinite  plane  which  is 
represented  by  the  ^-axis,  the  following  relation  is  easily  deduced: 

a2  =  d2  -  r2. 

Substituting  this  value  of  a  in  (4)  and  making  the  transformation  to 
polar  coordinates,  the  expression  for  the  surface  density  becomes 


Vd*  -  r2  i 

ff   =  -  .    -  (e) 

4-Trr         r  cos  <p  +  d 

This  gives  a  minimum  value  of  a  for  <p  =  o  and  a  maximum  value  for 
<f>  =  TT.  The  surface  distribution  on  the  infinite  plane  is  obtained  by 
putting  x  =  o  in  (4)  which  then  becomes 

*  =  ',9*  ~~^-  (6) 


WIRE  PARALLEL  TO  Two  PLANES  INTERSECTING  AT  RIGHT  ANGLES. 

The  equipotential  lines  and  lines  of  force  about  a  long  wire  parallel 
to  the  intersection  of  two  perpendicular  infinite  planes  are  given  by  the 
transformation 


where 

a  =  a  +  bi     and     0  =  a  —  bi. 


No.  6,] 


DETERMINATION  OF  CAPACITIES. 


436 


The  curves  in  the  z- plane  for  u  equal  to  a  constant  are  shown  in  Fig.  i. 
Near  the  point  (a,  b)  the  curves  approximate  very  closely  to  circles  so 
that  the  equipotential  line  C  in  Fig.  i  can  be  replaced  by  a  wire  of  circular 


Fig.  1. 


cross-section  without  any  appreciable  error  if  the  radius  r  is  small  as 
compared  to  the  distances  a  and  b.  Then  the  center  of  this  circle  can 
also  be  taken  as  the  point  (a,  b).  From  (7)  we  have 


ilog 


(x*  -  y  -  a"  +  ft2)2  +  4(*y  +  ab)2 
(x*  -  f  -  a2  +  62)2  +  4(xy  -  aft)2 


(8) 


Now  since  we  are  considering  only  the  case  where  r  is  small  as  compared 
to  a  and  b,  we  can  find  an  expression  for  the  potential  at  the  surface  of 
the  wire  by  placing  y  =  b  and  x  =  a  —  r  in  (8).  Then 


(r- 


-  2a) 


(9) 


Now  it  can  be  easily  proved  that  if  u  in  equation  (8)  represents  the 
potential  at  the  surface  of  the  conductor,  the  charge  on  it  will  be  one 
half  unit.  Hence  the  capacity  per  unit  length  between  the  wire  and  the 
two  planes  is 

i 


C  = 


U  —  UQ' 


where  UQ  is  the  potential  of  the  two  plane  conductors.     But  putting 


437  j.  w.  WOODROW.  [VOL.  xxxv. 

xy  =  o  in  (8)  gives  «0  =  o,  and  the  capacity  becomes 

I 


lo    V(r  -  2<z)2(r2 
°g 


(10) 


If  r  is  small  enough  that  it  may  be  neglected  in  comparison  with  a  in 
the  first  power,  the  expression  reduces  to 


This  same  transformation  may  be  used  for  finding  the  capacity  between 
two  horizontal  parallel  wires  at  equal  distances  above  the  earth,  the  one 
having  a  positive,  the  other  an  equal  negative  charge,  and  considering 
the  surface  of  the  earth  as  an  infinite  conducting  plane  at  zero  potential. 
In  this  case  we  have  for  the  capacity 


c  = 


where  u\  is  the  potential  of  the  wire  having  the  positive  charge  and  uz 
is  the  potential  of  the  other  wire.  To  find  the  value  of  w2,  let  y  =  b 
and  x  =  —  (a  —  r)  and  substitute  in  (8).  Then 

r«[(r  -  2a)*  +  46']  ,     . 


and  hence  uz  =  —MI;  which  gives  for  the  capacity 


>   rV(r  -  2aY  +  4&2 
or,  neglecting  r  as  compared  to  a  and  &,  we  have 


+ 


No.  6.J  DETERMINATION  OF  CAPACITIES.  438 

Two  WIRES  PARALLEL  TO  THE  EARTH  AND  ONE  DIRECTLY  ABOVE  THE 

OTHER. 

It  was  found  that  the  equipotential  lines  and  the  lines  of  force  about 
two  wires  parallel  to  the  earth  where  one  is  directly  above  the  other 
could  be  obtained  by  the  transformation 

(z2  +  a2  +  ad)  -  izd 
=  lo*(#  +  a«  +  «0+«r 

where  a  is  the  height  of  the  lower  wire  and  d  is  the  distance  between 
them.  This  is  the  case  where  the  lower  wire  bears  a  positive  charge 
and  the  upper  wire  a  negative  charge  and  the  radius,  r,  of  the  wire  is 
small  compared  to  a  and  d.  Then 

[x2  +  (y  -  a  -  d)*][**  +  (y  +  a)2] 
°Z[x*+(y  +  a  +  dnx2+(y-a)r 

The  potential  u\  of  the  lower  wire  is  found  by  putting  x  =  o  and  y  =  a-\-r 
in  (16);  hence 

(d  -  r)*(2a  +  r)2 


Likewise  to  obtain  the  potential  of  the  upper  wire,  substitute  x  =  o 
and  y  =  a  -\-  d  -}-  r  in  (16)  which  then  becomes 

r(2a  +  d+r)* 


(2a  +  2d 
Whence  the  capacity  for  this  system  is 


Y(d  -  r)(2a  +  r)(2a  +  2d  +  r)(d  +  r) 

2  log  —  — — : 


(19) 

.  /v—  -h  r)(2g  +  2J  +  r) 
4l°g-  r(2a  +  ^  4^T 

Neglecting  the  second  power  of  r 

C=—  =i=  .  (20) 

+  r)(a  +  d)+ar] 


If  we  take  a  as  infinite,  we  have  simply  the  case  of  two  parallel  wires 


439  J-  w-  WOODROW.  [VOL.  xxxv. 

for  which  the  capacity  is  known  to  be 

i 


C  = 


l  +  Vp-  r* 
4  log  - 


r 
where  2/  is  the  distance  between  them.     Or  neglecting  r2 


4  log-      4log- 

where  d  is  the  distance  between  the  wires.     Now  substituting  a  equal 
to  infinity  in  (20)  we  obtain 

C  =  —  —d,  (22) 

4log- 
which  agrees  with  the  former  result. 

THREE  PARALLEL  WIRES  ARRANGED  so  AS  TO  BE  AT  THE  CORNERS  OF 
AN  EQUILATERAL  TRIANGLE. 

In  transmitting  a  three-phase  alternating  current  by  an  overhead 
system,  the  wires  are  generally  arranged  so  that  they  are  at  the  corners 
of  an  equilateral  triangle.  We  shall  find  the  electrostatic  capacity  of 
such  a  system  when  the  total  charge  on  all  the  wires  is  zero.  There 
will  be  no  loss  of  generality  if  the  charge  on  one  of  the  wires  is  taken  as 
one  positive  unit  while  that  on  each  of  the  other  two  is  taken  as  one  half 
a  negative  unit.  Again  a  very  simple  transformation  can  be  found  which 
will  give  the  proper  lines  of  force  and  equipotential.  This  transformation 
is 

.      (s2  -  4<*2)  + 


where  the  distance  between  any  two  wires  is  2aV  3.     The  equipotential 
lines  will  be  found  from  the  equation 

1  .      [(«  -  a  V3)*  +  (y  +  afflfr  +  a  ^3)2  +  (y  +  a)2]       ,    , 
=  il°g"  [*«  +  (y  -  2a)*p  "'     (24) 

which  is  obtained  directly  fron  (23)  in  the  usual  way. 

In  the  above  the  origin  has  been  taken  at  the  intersection  of  the 
medians  of  the  triangle  and  the  wire  bearing  the  positive  charge  has  its 
center  at  the  point  (o,  2a),  while  the  other  two  wires  have  their  centers 


No.  6.]  DETERMINATION  OF  CAPACITIES.  440 


at  the  points  (a  V$,  —a)  and  (—aV$,  —a)  respectively.  Hence  to 
find  the  potential  of  the  first  wire  we  shall  place  x  =  o  and  y  =  20,  —  r 
in  (24)  as  for  these  small  values  of  r  the  equipotential  lines  are  approxi- 
mately circles.  Hence  we  obtain 


11 
«i  =  \  log  -  —  ^-  -  ,  (25) 

(I2<z2  -  6ar  +  r2)2 
=  Jlog-         ~^-        -.  (26) 

To  find  the  potential  of  the  wires   bearing   the   negative   charge,    let 

y  =  —  (a  —  Jr)  and  x  =  V  3(0  —  Jr)  and  we  have 


Hence  it  is  seen  that  #2  =  —  J«i;  and  the  electrostatic  capacity  of  the 
three  wires,  which  is  defined  to  be  I/MI  —  #2,  becomes 


/ 
log( 


rz 


(28) 
(29) 


If  these  wires  are  considered  parallel  to  the  earth  and  the  influence  of 
the  latter  is  considered  the  transformation  takes  the  form 


,  > 

*[(«  +  <«)«  -3*1  [«-*(<*  +  3*)]' 

where  ^  is  the  height  of  the  two  lower  wires  above  the  surface  of  the  earth. 
Then  the  expression  for  the  potential  is 


1}     ([**-  (y  -  d}*-  3a  ,    . 

1       «  2         222  -d-  3a)2]2* 


The  potential  of  the  upper  wire  which  bears  the  positive  charge  of  one 
unit  is  found  by  placing  x  =  o  and  y  =  d  +  30  —  r  in  (31)  ;  which  gives 

,.      [(3ft  ~  r?  +  3<*212  •  [2d  +  6a  -  r]« 
<  3*  -  r)2  +  3*2? 


As  before  it  can  be  shown  that 

«2  =  ~  J«i-  (33) 


44 1  J-  w-  WOODROW.  [VOL.  xxxv. 

t 

Hence  the  capacity  of  this  system  becomes 


(2d  +  6a-r)       /      (3<*  -  rY 
3log  r  '  \2rf +    a -r 


(34) 


However  for  all  practical  cases  r  is  very  small  as  compared  to  d  so  that 
we  may  neglect  r  in  (34)  wherever  it  is  added  to  d.     This  gives 


[- 


(35) 


Placing  d  equal  to  infinite  in  the  above  equation  will  give  the  capacity 
of  the  three  wires  alone.     This  then  is 

/  l/i2a2  -  6ar  +  r2  \  ' 
3log(-         -7-         -) 

which  is  the  same  value  found  in  equation  (29). 

It  is  also  easily  seen  that  the  value  of  the  capacity  found  in  (35)  is 
larger  than  that  in  (29),  as  was  to  be  expected. 

IMAGES  IN  A  CYLINDER. 
Let  us  consider  the  transformation 

R2  —  az  .     . 

"-^  (37) 


This  gives  for  u  __ 

V(ff  -  axY  +  a*y*  . 

...;        "  =  log  RV(x-a?^-      ;  (38) 

For  u  =  o,  we  have 


(R*  -  ax)*  +  aV  =  £2[(*  -  a)2  +  /], 
whence 

xz  +  yz  =  R2.  (39) 

That  is,  the  zero  potential  surface  is  a  cylinder  and  the  cross-section  in 
the  :ry-plane  is  a  circle  of  radius  R.     Again  from  equation  (38),  we  obtain 

(R*  -  axY  +  oV 

e  "  ~ 


-  a) 


No.  6.] 
and 

or 


DETERMINATION  OF  CAPACITIES. 


442 


yz  - 


aR2 


-    /l2 


-    2 


=  o, 


/ 
(*  ~ 


a2  -  £2)12 
TT-?2  J  • 


(40 


Hence  the  equipotential  lines  are  all  circles  with  their  centers  on  the 
#-axis  and  at  a  distance  from  the  origin  given  by 


The  radii  are  given  by 


e2»  -  i 
R2e2»-a2' 

e»R(a2  -  R2) 
R2e2"  -  a2    ' 


(42) 


in  which  the  positive  sign  is  to  be  used  for  values  of  u  greater  than 
u  =  log  (air)  and  the  negative  sign  for  values  less  than  that.     The 


Fig.  2. 

reason  for  this  is  quite  obvious  from  Fig.  2.     The  radius  becomes  infinite 
for  u  —  log  (a/r)  and  the  equipotential  curve  becomes  the  straight  line 


x  = 


20, 


Now  let  r\  be  the  radius  of  a  small  wire  bearing  a  charge  of  one  half 
unit  per  unit  length  placed  parallel  to  a  large,  earthed,  cylindrical  conduc- 
tor of  radius  R  and  let  d  be  the  distance  between  the  centers  of  the  two. 
Then  we  can  replace  the  cylinder  by  another  wire  bearing  a  negative 
charge  of  one  half  unit  without  any  change  in  the  electrostatic  field. 
To  find  the  radius  r*  and  the  position  of  this  latter  wire  replace  u  by  —  u 
in  equations  (41)  and  (42).  It  will  be  seen  that  r2  is  less  than  r\  as  might 


443  J-  w-  WOOD  ROW.  [VOL.  xxxv. 

be  expected.     For 

euR(a2  -  R2)  euR(a2  -  R2) 

ri  ~     R2e2u  -a2    '     r*~     a2e2u  -  R2    * 

Also  the  positions  of  the  centers  of  the  wires  will  be  given  by 

''  (44) 


It  is  to  be  understood  that  the  above  reasoning  only  holds  for  the 
case  where  very  long  and  large  cylinders  are  considered.  It  can  readily 
be  shown  that  the  method  of  images  does  not  apply  rigorously  to  the 
case  of  two  long  small  parallel  wires  at  any  considerable  distance.  That 
is,  as  suggested  earlier  in  this  paper,  the  electric  force  in  the  direction 
of  the  2-axis  must  be  so  small  that  it  may  be  neglected.  However  in 
this  as  in  the  general  theory  of  the  logarithmic  potential,  the  very  long 
wires  must  be  considered  as  finite  in  length  when  applying  the  test  of 
zero  potential  at  an  infinite  distance. 

Now  equation  (38)  may  be  used  for  finding  the  capacity  between  a 
wire  bearing  a  charge  and  an  earthed  wire  near  it.  First  consider  the 
case  where  the  small  wire  is  external  to  the  earthed  cylinder.  The  first 
of  equations  (43)  gives 

az  -  R2) 


(46) 


l  ~     R2e2u  -  a2 
from  which  we  find 

R2(e«R 


From  the  first  of  equations  (45) 

* 

whence 

2  =  ( 

1  =  eu 

Solving  for  eu, 


\(t\  Y\  J\.    )         |  \v~i  .    j.  •"    /  T^-    '    A  /.— \ 

e«  = -^—  ~ ,          (47) 

and 


Now  it  is  easily  proved  that  the  charge  on  the  wire  is  one  half  a  unit, 
so  that  the  capacity  of  this  system  is 


No.  6.]  DETERMINATION  OF  CAPACITIES.  444 


(dt  -  ri2  -  R2) 

2log- 

Likewise  the  capacity  between  the  internal  wire  and  the  cylinder 
may  be  found  from  the  second  of  the  equations  (44)  and  (45)  respectively. 
This  gives 


(S*  +  rt  -  df) 
2log" 

To  prove  that  the  above  expressions  have  the  proper  form,  place 
d  =  i  +  R  and  let  R  become  infinite;  that  is,  let  the  earthed  cylinder 
become  an  infinite  earthed  plane.  This  gives 


l  +  Vl2  -r2 

2  log  -      —j- 

which  is  the  identical  expression  previously  obtained  for  a  wire  parallel 
to  an  infinite  earthed  plane. 

An  expression  for  the  surface  distribution  over  the  earthed  cylinder  is 
very  easily  obtained.     From  equation  (37)  we  obtain 

dw  R2  -  a2 


dz      az2  -  z(R2  +  a2)  +  aR2' 
Taking  the  absolute  value  and  simplifying 

R2  -a2 


dw 
dz 


V[a(x2  -y2  +  R2)  -  x(R2  +  a2)]2  +  \y(2ax  -  R2  -  a2}2 
Transforming  to  polar  coordinates 

dw        R2  —  a2 

dz    ~  R(R2  -r-  a2  -  2aR  cos  <p) ' 
Hence 

j R2  -a2 

~  47r  R(R2  +  a2  -  2aR  cos  *>) 

and  a  can  be  calculated  for  any  particular  system  from  equation  (46). 
It  is  seen  that  the  maximum  value  of  a  is  for  <f>  =  o  and  the  minimum 
value  for  <p  =  IT. 


445  J-  w-  WOODROW.  [VOL.  XXXV. 

Two  CORE  CABLE. 
We  shall  next  consider  the  transformation 

(z  +  a)(z-b) 
•W  =  log^ rj — TfTx' 

This  gives 

M  =  *lo4*-a)°- 
from  which  the  zero  potential  curves  are  found  to  be 

x  =  o 
and 

*v  \        J[ 

The  latter  suggests  the  possibility  of  using  the  transformation  for  the 
cases  where  wires  are  encased  in  an  earthed  sheath  of  circular  cross 
section,  and  where  the  total  charge  on  the  cable  at  any  instant  is  zero. 


Fig.  3. 

The  following  results  are  for  air  as  the  dielectric,  but  of  course  the  results 
can  be  altered  to  fit  the  case  for  any  dielectric. 
If  the  radius  of  this  sheath  is  R,  we  have 

ab  =  R\ 
Replacing  b  in  the  original  equation  by  (R2/a)  gives 

(z  +  a)(az  —  R2) 
w  =  log  ,    _    .,          R2.  ,  (52) 

and  for  the  potential 

,  .      [(«  +  a-)2  +  y][(a*  ~  -R2)2  +  «VI  ,.,. 

«  =  2  log  [(x  _  fl),  +  y,][(ax  +  R1)2  +  flV]  •  (53) 


No.  6.]  DETERMINATION  OF  CAPACITIES.  446 

The  equation  of  the  equipotential  lines  becomes 

e*[(x  -  a)2  +  y*][(ax  +  R*Y  +  a?y*} 

=  l(x  +  a)2  +  y*][(ax  -  £2)2  +  a2?2]. 

These  curves  are  shown  in  Fig.  3.  In  many  cables,1  used  especially  in 
Europe,  a  bundle  of  wires  is  so  arranged  that  the  contour  exactly  coin- 
cides with  the  heavy  curves  AB  and  DE  shown  in  Fig.  3. 

If  a  =  R/3,  we  shall  have  AD  =  EF.     This  is  the  most  usual  condition. 
Substituting  R/3  for  a  in  (53),  we  obtain 


54 


Now  let  AD  =  EF  =  2d;  then  for  y  =  o,  x  =  d  we  obtain  the  potential 
of  the  bundle  of  wires  DE,  which  is 


+  SRd  -  ^d2 
°g  3#2  -  SRd  -  sd*  ' 

Likewise  the  potential  of  the  bundle  of  wires  AB  will  be  obtained  by 
placing  y  =  o  and  x  =  —  d.     Hence 

(3d  -R)(d 
log 


+  R)(d  - 

Hence  u^  =  —  u\  and  the  capacity  per  unit  length  between  the  two 
bundles  of  wires,  one  positively  the  other  negatively  charged,  surrounded 
by  an  earthed  cylinder  of  circular  cross-section  is 


SRd  I  '  (56) 


Another  case  of  interest  is  that  in  which  two  small  wires  are  encased 
in  the  circular  sheath.  As  is  seen  in  Fig.  3,  the  smaller  equipotential 
lines  approximate  to  circles.  Making  this  approximation,  we  shall 

1  See  Russell's  Alternating  Currents,  Vol.  i,  Chapters  IV.  and  V. 


447  J-  w-  WOOD  ROW.  I  VOL.  XXXV. 

obtain  the  potential  of  the  wire  bearing  the  positive  charge  by  placing 
y  —  o  and  x  =  a  —  2^/3  in   (53),  which  gives  the  case  for  a  = 
Hence 


(2r  -  6a)(3a2  -  2ar  - 
:1°g-  ' -  (57> 


Then  placing  a  =  R/3,  we  have 

(R  -  r)(^R  -  r) 
r(5R  -  r) 

And  the  capacity  between  the  two  wires  within  the  earthed  sheath  is 

i 


(R  -  r)(4*  -  r) ' 
4l°g-     r(5R-r) 


(58) 


It  is  to  be  understood  that  this  latter  form  is  an  approximation  that  can 
be  used  only  for  small  wires  so  placed  that  the  distance  from  the  surface 
of  one  wire  to  the  surface  of  the  other  is  equal  to  the  distance  from  the 
inner  surface  of  the  metal  sheath  to  the  surface  of  the  nearest  wire. 
However  the  method  can  be  adapted  to  other  conditions  by  taking  the 
proper  relations  between  a,  r,  and  R. 

THREE  CORE  CABLES. 

A  transformation  was  found  which  would  give  equipotential  lines  which 
very  nearly  coincide  with  those  in  the  clove-leaf  type  of  three-core  cable. 
A  diagram  of  this  cable  is  shown  in  Russell's  Alternating  Currents, 
Vol.  I.  This  transformation  is 


((z*  -  R*)  +  Rzi]  -  (z  - 
log      2  _         .  _       >  ' 


where  the  distance  between  the  surfaces  of  the  bundles  of  wires  is  equal 
to  the  distance  from  the  inner  surface  of  the  enclosing  metal  sheath 
to  the  surface  of  one  bundle  of  wires.  The  charge  on  one  of  the  con- 
ductors is  one  positive  unit,  while  each  of  the  other  two  has  a  negative 
charge  of  one  half  unit.  Then  the  equation  of  an  equipotential  line 
becomes 


,  1  ,,  , 

°g      **22**       zz2  '    (     } 


[xz+(y-R)z]2 
Now  if  d  is  the  distance  from  the  center  of  the  circular  cylinder  to  the 


No.  6.]  DETERMINATION  OF  CAPACITIES.  448 

outer  surfaces  of  the  bundles  of  wires,  an  expression  for  the  potential 
of  the  wire  bearing  the  positive  charge  will  be  obtained  by  substituting 
x  =  o  and  y  =  d  in  (60).  This  gives 

HI  =  log 


-  d)V/(R  +  d)2  -  Rd  1 

(61) 


Now  it  can  be  proved  that  the  potential  of  the  conductors  bearing  the 
negative  charge  is 


Hence  the  capacity  of  the  system  is 


/  T"»  7  [          /   T"»  1  7\  O  T-»     T  \  \  J 


/  4R 

°8\R- 


4R-  d  (R  +  d)*  -  Rd 


R  -  d      X  UR  +  d)2  - 


3 


If  the  conductors  are  small  wires  of  circular  cross-section,  and  radius  r, 
a  close  approximation  to  the  value  of  the  capacity  will  be  obtained  by 
substituting  d  =  %R  +  r  in  (62).  For  this  condition  then 

C  =  -  (63) 

,log/7*-2r         7^  +  8^  +  4^ 
5  V  2R  -  4r  '  \f  iSR*  +  $Rr  +  r*l 

It  may  seem  at  first  that  too  many  approximations  have  been  made  in 
this  paper,  but  a  closer  examination  will  show  that  the  results  obtained 
by  using  the  formulae  derived  will,  for  nearly  all  practical  cases,  be  more 
accurate  than  the  measurements  from  which  the  calculations  are  made. 
In  the  cases  of  the  cables  if  the  wires  have  the  shape  of  the  equipotential 
lines,  the  results  will  be  exact. 

In  conclusion  I  wish  to  thank  Dr.  J.  Kunz  and  Professor  E.  J.  Townend 
for  their  many  helpful  suggestions  during  the  investigation  of  the  above 
problems. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
August,  1912. 


Reprinted  from  School  Science  and  Mathematics,  Vol.  13,  1913. 

Pages  421-422. 

THE  PROJECTION  OF  "THE  GUINEA  AND  THE  FEATHER" 

EXPERIMENT. 

BY  A.  P.  CARMAN., 
^  University  of  Illinois. 

The  usual  apparatus  for  "the  guinea  and  the  feather"  experi- 
ment, to  show  all  that  all  bodies  fall  with  the  same  acceleration  in 
a  vacuum,  consists  of  a  glass  tube  three  or  four  inches  in  diameter, 
with  a  eoih  and  a  feather  inside.  Upon  inverting  the  exhausted 
tube  quickly,  those  near  by  can  see  that  the  two  objects  fall  some- 
what together.  The  objects  however  often  strike  the  sides  of  the 


tube,  and  the  observation  is  that  the  two  objects  "would"  fall  to- 
gether if  they  fell  freely.  For  a  large  class,  the  experiment  is 
also  unsatisfactory  because  most  of  the  class  see  nothing.  The 
experiment  is  so  important  in  explaining  "weight"  and  "mass/' 
and  has  such  historical  importance  that  the  writer  and  his  as- 
sistants arranged  apparatus  so  that  the  two  objects  are  released 
at  the  same  instant  and  fall  freely,  and  so  that  a  large  class 
can  see  the  occurrence  by  the  direct  shadow  method  of  projection. 
The  arrangements  simple,  but  it  has  been  suggestive  and  useful 
to  some  who  have  seen  it,  and  so  it  is  described  here. 


422  SCHOOL   SCIENCE   AND   MATHEMATICS 

An  air-tight  rectangular  box  of  metal  and  glass  was  made, 
(Figure)  forty  inches  long  and  with  cross-section  six  inches 
square.  The  section  could  just  as  well  be  reduced  to  four  inches 
square.  The  top,  bottom  and  two  of  the  opposite  sides  are  of  cast 
iron,  the  other  two  sides  are  of  heavy  plate  glass  cemented  to  the 
planed  iron  surfaces,  and  in  addition  held  in  place  by  clamps.  A 
hose  connection  with  stop-cock  C  is  placed  in  one  side  for  ex- 
hausting the  air.  There  is  a  three  inch  circular  opening  in  the 
top,  and  this  is  closed  by  a  plane  metal  plate  M,  the  fit  of  which 
is  made  air-tight  by  a  flat  rubber  ring.  Through  this  plate,  there 
are  insulated  electrical  binding  posts  and  connectors,  .which  carry 
on  the  under  side  a  loop  of  small  fuse  wire.  On  this  fuse  wire 
are  hung  a  feather  F  and  a  bullet  B.  These  are  released  ai  the 
same  instant  by  melting  the  fuse  wire  with  an  electric  current. 
The  box  is  placed  in  the  light  of  the  projection  lantern,  so  that 
the  shadows  of  the  feather  and  bullet  are  distinct  on  the  screen. 
When  the  objects  are  released  by  making  the  electric  circuit,  they 
fall,  so  far  as  the  eye  can  tell,  absolutely  together,  if  the  box  is 
exhausted.  The  simultaneous  fall  can  be  seen  clearly  by  every- 
one in  the  lecture  room.  An  additional  advantage  of  this  ap- 
paratus is  that  it  is  separate  from  the  air  pump  and  is  always 
ready. 


Reprinted  from  School  Science  and  Mathematics,  Vol.  13,  1913. 

Pages  1-9. 


SOME  RECENT  PHYSICAL  THEORY.i 

BY  ALBERT  P.  CARMAN, 
University  of  Illinois. 

The  announcement  by  Wilhelm  von  Rontgen  in  December, 
1895,  of  his  discovery  of  a  new  kind  of  radiation,  created  an 
immediate  and  widespread  interest  which  has  probably  not  been 
exceeded  in  the  history  of  science.  But  the  importance  of  that 
event  was  far  greater  than  the  announcement  of  a  striking  and 
astonishing  discovery.  The  subsequent  developments  of  physics 
and  chemistry  show  that  Rontgen's  discovery  marks  the  practical 
beginning  of  a  new  era  in  physical  science.  While  our  knowl- 
edge of  the  nature  of  X-rays  has  increased  little  beyond  what  we 
learned  in  the  first  few  months  after  their  discovery,  the  investi- 
gations started  and  suggested  by  Rontgen's  discovery  have 
revolutionized  our  concepts  and  theories  in  nearly  every  field  of 
physics.  Thus  Sir  J.  J.  Thomson  was  started  with  a  new  im- 
pulse into  the  investigations  of  the  nature  of  the  cathode  rays 
and  the  mechanism  of  the  electrical  conductivity  of  gases,  and 
these  investigations  led  directly  to  the  discovery  of  the  cor- 
puscle or  electron.  In  France,  Becquerel  was  inspired  to  study 
the  fluorescent  effects  of  many  minerals,  and  the  next  year  after 
Rontgen's  announcement  came  the  epoch  making  discovery  of 
the  Becquerel  rays,  a  phenomenon  which  might  have  remained 
unknown  for  another  generation,  had  it  not  been  for  the  sug- 
gestion of  the  Rontgen  rays.  Following  this  lead,  we  have  the 
great  investigations  of  the  Curies,  Rutherford,  Ramsey,  and 
many  others  in  the  subject  of  radioactivity  and  of  the  nature  of 
the  chemical  elements.  The  concepts  thus  introduced  and  the 
methods  made  possible  by  the  new  phenomena,  have  enabled 
physicists  and  chemists  to  re-open  old  investigations,  and  the 
facts  thus  revealed  have  given  us  new  interpretations  of  many 
old  results  that  were  thought  complete.  We  are  still  in  the 
midst  of  this  scientific  era,  and  much  remains  speculative  and 
unsettled,  yet  it  has  seemed  well  to  spend  a  short  time  in  discuss- 


iRead    at    the    meetinp    of    the    Central    Association    of    Science    and    Mathematics 
held  with   Northwestern   University,   Evanston,    111.,   Nov.    29,    1912. 


2  SCHOOL   SCIENCE   AND    MATHEMATICS 

ing  some  of  the  newer  concepts  which  must  affect  our  beginning 
statements  and  definitions,  and  hence  must  interest  us  most 
vitally  as  students  and  teachers  of  physics. 

Perhaps  no  concept  ever  dominated  science  so  completely  as 
did  the  concept  of  the  aether  dominate  physics  during  the  nine- 
teenth century.  The  aether  was  the  medium  of  which  eminent 
thinkers  and  writers  told  us  that  we  knew  more  about  than  we 
do  about  air  or  any  other  form  of  matter.  By  this  medium  we 
explained  the  action  and  nature  of  light,  the  transmission  of 
electrical  and  magnetic  induction,  and  even  of  gravitational 
force.  Matter  itself  was  supposed  to  be  whirls  or  vortices  in 
this  aether,  and  positive  and  negative  electricity  were  simply 
boundary  conditions  due  to  the  displacements  of  the  aether.  Many 
of  the  greatest  minds  of  the  nineteenth  century  spent  their  best 
energies  in  the  development  of  a  physics  of  the  aether.  Such 
intellectual  giants  as  Fresnel,  Kelvin,  Maxwell,  Stokes,  Mac- 
Cullough,  Helmholtz,  Hertz  and  Poincare  worked  at  the  prob- 
lems of  this  universal  medium  which  was  thus  to  advance  us 
further  in  solving  the  mystery  of  the  universe.  The  aether  was 
primarily  a  concept  to  explain  the  propagation  of  such  periodic 
disturbances  as  visible  and  invisible  light.  The  concept  of  a 
luminous  aether  was  first  stated  in  a  tangible  form  by  Christian 
Huygens  and  Robert  Hooke  in  the  seventeenth  century,  but  it 
was  not  until  the  very  beginning  of  the  nineteenth  century  that  it 
displaced  the  corpuscular  or  emission  theory  which  we  ascribe, 
perhaps  improperly,  to  Sir  Isaac  Newton.  Then  came  the  bril- 
liant discoveries  of  the  interference  of  light  by  Dr.  Thomas 
Young  in  England,  and  Augustin  Fresnel  in  France,  with  their 
direct  explanation  on  the  undulatory  aether  hypothesis.  This 
was  followed  by  Fresnel's  work  in  the  polarization  and  double 
refraction  of  light,  so  that  before  Fresnel's  death  in  1827,  there 
were  few  who  questioned  the  undulatory  theory  of  light  and  the 
existence  of  a  luminous  aether.  But  there  were  difficulties  in  the 
concept,  and  it  called  for  all  the  skill  of  Kelvin  and  other  great 
mathematical  physicists  of  the  middle  of  the  last  century  to 
develop  the  so-called  "elastic  solid  theory"  of  the  aether,  which 
should  meet  the  facts  of  with  even  approximate  satisfaction. 

During  these  same  years,  Michael  Faraday  had  been  develop- 
ing his  theory  of  electric  and  magnetic  fields,  and  had  given  to 
science  his  great  concept  of  lines  of  electric  force.  Faraday  did 
not  at  first  assume  any  medium  for  the  lines  of  force,  and  even 
as  late  as  1851,  he  seems  to  have  had  his  doubts  about  the 


RECENT  PHYSICAL   THEORY  3 

necessity  of  an  aether  for  the  transmission  of  electrical  and 
magnetic  forces  across  space.  While  he  suggested  that  the 
luminous  aether  might  ''have  other  uses  than  simply  the  convey- 
^ance  of  radiation,"  and  might  be  the  vehicle  of  magnetic  force,  it 
was  not  Faraday,  but  James  Clerk  Maxwell,  who  developed  the 
concept  of  the  electromagnetic  luminous  aether.  Maxwell  took 
up  the  problem  which  was  placed  before  him  by  Faraday's  "Ex- 
perimental Researches  in  Electricity."  He  was  equipped  for  the 
work  by  his  training  in  the  University  of  Cambridge  which  has 
for  centuries  been  one  of  the  world's  great  mathematical 
centers  and  he  developed  a  theory  which  has  been  the  admira- 
tion of  both  physicists  and  mathematicians.  Maxwell's  electro- 
magnetic theory  identified  electrical  and  magnetic  phenomena  as 
disturbances  in  the  same  medium  as  light,  and  indeed  made 
light  an  electromagnetic  wave  in  the  aether.  This  theory  gained 
recognition  slowly,  but  after  1887  and  1888,  when  Heinrich 
Hertz  demonstrated  by  his  brilliant  experiments  the  existence 
and  properties  of  electric  waves,  there  seemed  to  be  nothing 
more  firmly  fixed  in  physics  than  the  existence  of  an  electromag- 
netic luminous  aether.  Thus  Sir  Oliver  Lodge  in  his  book  on 
Modern  Views  of  Electricity,  edition  of  1899,  describes  the  aether 
as  "one  continuous  substance  filling  all  space ;  which  can  vibrate  as 
light ;  which  can  be  sheared  into  positive  and  negative  electricity ; 
which  in  whirls  constitutes  matter;  and  which  transmits  by  con- 
tinuity and  not  by  impact  every  action  and  reaction  of  which  mat- 
ter is  capable."  A  theory  which  was  so  dominant  with  the  most  ad- 
vanced and  profound  thinkers  in  physical  science,  naturally  came 
to  be  the  view  presented  in  the  manuals  of  physics,  so  that  we  find 
the  aether  concept  of  electricity  and  light  was  the  view  presented  in 
our  most  progressive  elementary  text-books  of  scarcely  a  decade 
ago.  But  while  these  elaborate  and  extensive  theories  of  the  aether 
were  held  generally,  there  were  some  thinkers  who  felt  that  the 
experimental  foundations  were  neither  broad  nor  sure  enough  for 
such  a  big  structure  of  theory.  Thus  Lord  Salisbury,  in  the  Pres- 
idential address  before  th,e  British  Association  for  the  Advance- 
ment of  Science  in  1894,  describes  the  aether  as  simply  the  subject 
of  the  verb  "to  undulate."  That  is,  he  calls  attention  to  the  fact 
that  the  aether  is  a  concept  to  explain  the  transmission  of  light 
waves,  and  that  is  all  we  really  know  about  it.  The  rest  is 
speculation. 

One  of  the  greatest  difficulties  of  the  aether  theory,  was  the 


4  SCHOOL   SCIENCE   AND   MATHEMATICS 

explanation  of  the  nature  of  the  electric  charge  as  it  appears  in 
electrolysis.  The  explanation  of  the  electric  current  through 
metallic  conductors  in  the  Maxwell  theory,  was  certainly  not 
simple,  though  it  gave  a  possible  solution,  but  the  passage  of 
electricity  through  an  electrolyte  was  confessedly  incomplete. 
Much  more  incomplete  was  the  theory  of  electric  discharge  across 
gases.  These  phenomena,  we  are  told,  greatly  interested  Max- 
well, but  the  whole  subject  of  discharge  through  gases  occupies 
but  a  few  short  sections  in  his  great  "Treatise  on  Electricity  and 
Magnetism."  While  Faraday,  Pliicker  and  others  had  fixed  some 
of  the  fundamental  facts  of  discharge  in  vacuum  tubes,  yet  at 
the  time  of  the  publication  of  Maxwell's  treatise  in  1873,  the 
facts  known  were  too  fragmentary  and  indefinite  to  form  the 
basis  for  any  general  theory.  At  the  time  of  Rontgen's  dis- 
covery, there  had  sprung  up  a  renewed  activity  in  the  investiga- 
tion of  the  phenomena  of  electric  discharges  in  exhausted  tubes. 
Lenard  had  discovered  rays  that  penetrated  aluminum  windows 
in  the  tube,  and  J.  J.  Thomson  had  already  begun  his  epoch 
making  investigations  in  this  field.  Rontgen's  startling  discov- 
ery gave  the  new  impulse  to  Thomson's  work  and  this  resulted 
in  the  atomic  or  electron  ^  theory  of  electricity.  The  electron 
theories  that  followed  have  completely  displaced  the  aether  theories 
for  many  phenomena.  Thus  the  electric  charge  is  no  longer  re- 
garded as  a  shear  of  the  aether,  but  as  a  collection  of  electrons ; 
the  electric  current  in  a  wire  becomes  a  flow  of  electrons,  and  not 
a  breaking  down  of  the  aether  strains  along  the  metallic  wire ; 
an  elementary  or  molecular  magnet  is  no  longer  due  to  aether 
whirls,  but  is  due  to  the  rotation  of  one  or  more  electrons  about 
the  material  atom.  The  asther  vortex  theory  of  matter  of  Kelvin 
and  Helmholtz  has  been  replaced  by  the  corpuscular  theory  of 
matter  of  J.  J.  Thomson.  The  inertia  of  matter,  thus  becomes 
the  electromagnetic  inertia  of  the  moving  electrons  of  which 
all  matter  is  built  up.  Within  a  little  over  a  decade,  the  corpus- 
cular theory  developed  by  Thomson  and  his  school  displaced  a 
large  part  of  the  physics  of  the  electric  aether  which  the  men  of 
the  19th  century  built  up  with  such  great  labor.  The  investiga- 
tions by  Rutherford  and  the  Curies  in  radioactivity  contributed 
largely  to  this  revolution  of  our  concepts.  Rutherford  showed 
that  radium  gave  off  three  types  of  rays,  and  that  two  of  them, 
the  a  and  /?  rays,  are  corpuscular  or  atomic  in  nature.  The 
third  type  of  rays,  the  y  rays,  it  has  been  commonly  thought 
are  the  same  as  the  X-rays  of  Rontgen,  and  these  have  been 


RECENT  PHYSICAL   THEORY  5 

thought  of  as  pulses  of  the  aether  produced  by  impacts  of  elec- 
trons. But  even  here,  there  has  arisen  a  question  of  the  necessity 
of  sether,  for  a  brilliant  experimenter  Professor  Bragg  of  Leeds, 
believes  that  he  has  shown  that  the  y  rays  are  corpuscular  or 
atomic.  If  the  y  rays  are  corpuscular,  then  Bragg's  conclusion  is 
that  X-rays  are  corpuscular  and  not  aether  pulses.  This  starts 
another  question,  for  the  X-rays  and  the  ultra  violet  light  show 
many  similar  properties  and  so  we  are  led  to  ask,  is  not  ultra 
violet  light  corpuscular  as  well  as  the  X-rays?  And  if  ultra  violet 
light  is  corpuscular,  why  is  not  all  light  and  radiation  to  be  con- 
sidered as  corpuscular.  Bragg's  concept  of  the  y  rays  is  that 
they  are  doublets  of  positive  and  negative  corpuscles,  so  that  the 
periodic  character  of  such  a  radiation  might  come  easily  as  a  con- 
sequence of  the  vibration  of  the  advancing  doublets.  If  this  bold 
speculation  prove  to  be  true,  we  shall  be  back  to  a  Newtonian  cor- 
puscular theory  of  light,  and  the  concept  of  an  aether  would  be 
rendered  still  more  unnecessary. 

But  how  explain  the  existence  of  lines  of  electric  and 
magnetic  force  in  a  vacuum?  The  aether  theory  said,  "they  are 
made  of  the  aether,  the  medium  which  fills  all  space  and  through 
which  light  is  propagated — that  is,  they  are  the  lines  of  strain- 
and  stress  in  the  intervening  medium."  The  newer  school  seem 
to  have  gone  back  to  Faraday's  very  first  tentative  ideas  of  lines  of 
force,  and  to  give  these  lines  an  objective  existence  independent 
of  any  medium.  Thus  Mr.  Norman  Campbell  in  his  recent 
book,  entitled  "The  Principles  of  Electricity,"  says :  "Lines  of 
force  are  just  lines  of  force  independent  for  their  existence  of 
all  surrounding  bodies,  and  there  is  no  more  to  be  said  about 
them.  If  lines  of  force  passing  through  sulphur  are  not  made 
of  sulphur,  there  is  no  need,  when  the  lines  pass  through  a 
vacuum  to  imagine  the  vacuum  filled  with  a  substance  of  which 
the  lines  may  be  made;  in  other  words,  our  electrical  theory, 
so  far  from  providing  additional  support  for  the  conception  of 
the  aether  filling  all  space,  does  not  require  such  a  conception  at 
all.  All  it  needs  is  the  conception  of  lines  of  force ;  where  there 
are  no  lines  there  is  no  need  for  the  presence  of  anything  at  all. 
We  do  not  require  to  imagine  present  everywhere  a  substance  of 
which  the  lines  of  force  may  be  made  when  charged  bodies  come 
into  the  neighborhood,  for  the  bodies  bring  their  own  lines  with 
them,  ready  made  and  unalterable."  He  says  further  in  emphasis, 
"The  idea  that  an  aether  existing  everywhere  is  needed  for  Fara- 
day's theory  is  not  necessary;  all  that  is  necessary  are  the  lines 


6  SCHOOL   SCIENCE   AND   MATHEMATICS 

of  force,  which  are  not  made  of  the  medium  through  which  they 
pass."  Mr.  Campbell,  whom  we  are  thus  quoting  represents 
views  which  are  more  radical  in  details  than  some  physicists  agree 
to,  but  certain  it  is,  that  the  electrical  and  magnetic  aether,  even 
if  we  call  intervening  space  by  that  name,  is  an  entirely  different 
conception  from  that  held  so  generally  a  dozen  years  ago  or  less, 
and  which  still  persists  in  text-books. 

We  turn  now  to  an  entirely  different  line  of  inquiry — that  is 
the  investigation  of  the  radiation  from  a  black  body.  When  a 
blackened  body,  such  as  a  carbon  filament,  is  raised  in  tempera- 
ture, it  gives  off  radiant  energy  which  increases  in  amount  and  also 
in  frequency  as  the  temperature  rises.  The  law  of  radiation 
from  an  ideal  "black  body,"  that  is,  from  a  body  which  radiates 
and  absorbs  perfectly,  has  been  studied  by  many  physicists  and 
numbers  of  theoretical  formulae  have  been  proposed.  About 
1895,  a  group  of  German  physicists,  prominent  among  whom  were 
Professors  Lummer,  Pringsheim  and  Kiirlbaum  of  Berlin,  began 
to  give  us  exact  experimental  results  on  the  radiation  and  the 
temperature  in  the  case  of  a  uniformly  heated  cavity  which 
was  nearly  closed,  and  which  for  all  practical  purposes  realized 
Kirchhoff's  ideal  black  body.  These  and  later  results  have 
afforded  a  guide  and  test  to  the  theoretical  radiation  formulas  of 
Wien,  Rayleigh,  Jeans,  Planck,  Kunz  and  others.  Of  these 
formulas,  that  of  Planck  has  been  most  widely  accepted,  though 
the  firmness  of  its  theory  has  been  questioned  and  some  think 
the  agreement  with  experiment  to  be  accidental  and  apparent 
and  not  real.  Planck  started  with  the  concept  of  the  electro- 
magnetic origin  of  radiant  energy.  He  assumes  it  due  to  vibrat- 
ing electrons  in  the  atom  and  takes  Hertz  electric  oscillator  as 
the  type  of  the  electronic  oscillator.  This  is  the  common  type 
familiar  to  students  of  electric  waves  and  simple  wireless  teleg- 
raphy. As  stated  the  formula  thus  derived  agrees  fairly  well 
with  our  present  experimental  results  for  a  wide  range  of  tem- 
peratiures  and  hence  has  received  wide  acceptance.  The  most 
striking  fact  of  Planck's  radiation  theory  is,  however,  that  it  leads 
to  Planck's  "quantum"  or  atomic  hypothesis  of  radiant  energy. 
This  hypothesis  says  that  radiant  energy  is  not  to  be  considered 
as  infinitely  divisible  and  continuous,  but  as  discrete  and  made 
up  of  a  great  number  of  finite  and  probably  equal  parts,  called  by 
Planck,  "quanta."  Professor  Einstein  of  Zurich,  who  is  one 
of  the  first  of  living  mathematical  physicists,  has  gone  beyond 
Planck's  conception,  and  says  that  a  ray  of  light  consists  of 


RECENT  PHYSICAL   THEORY  7 

innumerable  atoms  of  energy  or  light  quanta,  that  is,  that  the  light 
exists  in  space  in  discreet  light  atoms,  or  quanta,  and  is  not  con- 
tinuous as  the  aether  wave  theory  assumes. 

It  is  not  possible  in  a  short  paper  to  present  the  detailed  rea- 
sons which  have  led  Planck,  Einstein  and  others  to  these  new 
views  of  the  nature  of  radiant  energy.  The  papers  of  Planck, 
Einstein,  Sommerfeld,  Nernst  and  others  must  be  studied  by 
one  who  wishes  to  understand  how  firm  a  hold  this  atomic  theory 
of  radiant  energy  and  light  has  upon  a  large  group  of  the  most 
profound  thinkers  in  physical  science  today.  Certainly  if  we 
are  to  accept  an  atomic  theory  of  electricity  and  an  electronic 
theory  of  matter,  then  there  is  nothing  strange  or  absurd  in  an 
atomic  or  corpuscular  theory  of  the  light  and  radiation  coming 
from  matter,  for  Zeeman,  Lorentz  and  others  have  shown  the  close 
connection  between  the  vibrating  electron  and  the  emitted  light. 
It  would  however  sound  strange  to  Helmholtz  and  the  physicists 
of  his  generation  to  learn  that  we  have  come  back  to  a  theory  so 
closely  resembling  the  Newtonian  emission  theory.  We  thus  see 
that  the  electron  theories  are  leading  us  to  ideas  of  discrete 
quantities  of  not  only  electric  but  also  light  energy.  This  is 
manifestly  not  in  accord  with  th,e  concept  of  a  continuous  aether. 

One  of  the  fundamental  questions  about  the  aether  has  always 
been,  is  the  aether  stationary  or  does  it  move  with  the  earth? 
The  experiments  on  this  question  are  so  contradictory  that  a 
whole  group  of  leading  scientific  men  have  been  led  to  deny 
not  only  the  existence  of  the  asth,er,  but  also  to  revise  the  "common 
sense"  ideas  of  time  and  space  which  have  always  been  used 
by  physicists,  whatever  their  metaphysical  creed  might  be.  On 
one  hand  we  have  the  famous  aberration  observations  of  James 
Bradley  made  in  1728,  that  a  ray  of  light  from  a  star  appears  to 
come  at  a  slanting  angle.  This  is  explained  directly  as  due  to 
the  composition  of  the  velocities  of  the  earth  and  of  the  light. 
Thus  if  the  light  is  a  disturbance  in  the  aether,  the  aether  must  be 
stationary  in  reference  to  the  earth.  On  the  other  hand,  we  have 
the  recent  experiments  of  Michelson  and  Morley  and  Miller,  of 
Brace,  and  of  others,  which  show  that  the  apparent  velocity  of  a 
ray  of  light  does  not  depend  upon  whether  the  direction  of  the 
light  is  the  same  as  that  of  the  earth  or  not.  The  direct  inter- 
pretation of  these  last  experiments  is  that  there  is  no  relative 
motion  of  the  aether  and  of  the  earth.  It  is  probable  that  these 
experiments  on  aether  drift  have  been  with  most  physicists  the 
greatest  reason  for  questioning  the  aether  concept  of  luminous 


8  SCHOOL   SCIENCE   AND   MATHEMATICS 

transmission.  Thus  Fitzgerald  and  Lorentz  have  suggested  a 
possible  explanation  in  assuming  that  material  bodies  shrink 
in  the  direction  of  the  aether  drift,  and  hence  the  change  in  the 
light  velocity  would  be  hidden.  This  is  however  giving  us  a 
meter  bar  of  shifting  length,  and  most  of  us  like  to  think  of 
something  as  fixed.  A  recent  writer  says,  "Almost  any  experi- 
mental result  can  be  reconciled  with  almost  any  theory  if  sufficient 
subsidiary  assumptions  are  made ;  the  only  question  is  whether  it 
is  worth  making  them."  As  said  above,  many  do  not  think  the 
original  concept  is  worth  making  the  necessary  subsidiary  as- 
sumptions. The  question  involved  in  a  stationary  or  moving 
aether  is  a  very  big  one,  and  it  is  mentioned  here  simply  as  another 
evidence  of  the  drift  away  from  the  aether  concept,  in  its  old  form 
at  least. 

From  what  we  have  been  saying  it  will  be  seen  that  there  is 
at  present  a  decided  tendency  in  physics  to  go  back  to  the  older 
separate  entities  and  to  abandon  the  continuous  fluid  ideas  as- 
sociated with  the  aether  concept.  Thus  we  have  the  electron 
instead  of  Maxwell's  aether  "displacement"  and  if  Planck's  radia- 
tion theory  is  to  be  accepted,  we  have  a  corpuscular  concep- 
tion of  energy.  An  interesting  extension  of  this  same  idea,  is 
given  in  Professor  Callendar's  address  before  the  Physics  Sec- 
tion of  the  B.  A.  A.  S.  in  its  meeting  at  Aberdeen  last  August. 
Professor  Callendar  suggests  that  recent  discoveries  point  to- 
wards a  material  theory  of  heat,  and  he  then  proceeds  to  show 
that  a  modified  caloric  theory  of  heat  affords  reasonable  ex- 
planations of  thermal  phenomena.  He  further  advances  the  spec- 
ulation that  this  caloric  may  be  neutral  corpuscles.  That  the 
countrymen  and  students  of  Kelvin,  Joule,  Tait,  Rankine  and 
Tyndal  should  entertain  with  scientific  seriousness  the  discussion 
of  a  corpuscular  theory  of  heat  by  one  of  their  leading  physicists, 
is  indeed  very  significant.  If,  however,  an  atomic  or  quanta 
theory  of  radiant  energy  is  to  be  accepted,"  it  is  certainly  not 
many  steps  to  a  caloric  theory  of  heat. 

It  is  thus  evident  that  we  are  in  a  period  of  new  fundamental 
theories  in  physics.  To  the  student  of  physics  it  is  a  most  inter- 
esting and  stimulating  time,  with  opportunities  and  invitations 
for  telling  work  in  nearly  every  field  of  physics.  To  the  teacher 
who  is  stating  and  presenting  the  elements  of  the  subject,  the 
situation  is  not  simple.  To  keep  abreast  of  the  advances  in 
fundamental  concepts,  and  still  keep  on  safe  ground  is  not  easy. 
Further,  the  theory  that  appears  simplest  to  present  may  not  be 


R  EC  EXT  PHYSICAL   THEORY  0 

that  which  is  nearest  the  truth.  Thus  Professor  Callendar  sug- 
gests that  the  kinetic  theory  of  heat  has  come  to.  be  adopted  to 
the  exclusion  of  the  material  idea,  because,  quoting  his  words, 
"The  kinetic  theory  is  generally  preferable  for  elementary  ex- 
position." In  this  .particular  case  most  of  us  are  not  yet  ready 
to  abandon"  the  essentials  of  a  kinetic  theory  of  heat,  but  the 
idea  suggested  of  giving  a  theory  because  it.  is  "preferable  for 
elementary  exposition"  raises  a  question.  There  are  indeed  those 
who  hold  that  a  theory  is  simply  scaffolding  and  not  a  serious 
attempt  to  build  a  permanent  structure.  There  is  a  system  of 
philosophy  which  claims  to  be  copying  the  methods  of  natural 
science  which  confesses  that  its  explanations  are  purely  specula- 
tive and  cares  nothing  for  reality.  Indeed  it  is  claimed  that  the 
number  of  possible  working  theories  of  material  phenomena  is 
indefinite  and  that  the  theory  that  we  adopt  is  simply  a  question 
of  convenience  in  thinking.  The  general  introduction  of  such 
metaphysical  ideas  into  physics  would  be  fatal  to  advance.  As 
students  and  teachers  of  physics,  we  must  believe  and  teach  that 
a  physical  theory  is  a  real  explanation  of  real  phenomena,  if  the 
physics  of  this  century  is  to  equal  and  excel  the  triumphs  of 
the  physics  of  the  last  century. 


Determination  theorique   de   la   variation   de  la  masse  de  1'  electron   en 

fonction  de  la  vitesse 

JACOB  KUNZ 

ABSTRACT 

Archives  des  sciences  physiques  et  naturelles  de  Geneve,  tome  XXXV, 

1913,  p.  28. 


It  is  assumed  in  this  article  that  the  electromagnetic  field  surrounding 
a  moving  electron  is  endowed  with  mass,  momentum  and  energy.  The 
expression  for  the  mass  per  unit  volume  as  suggested  by  the  pressure  of 
light,  is 

uk2E2sin2'(> 
mi  =— 

47T 

The  resultant  electromagnetic  mass  depends  on  the  shape  of  the  electron. 
If  we  assume  that  the  electron  during  the  motion  remains  spherical  we 
obtain  for  the  mass: 


If  the  electron  contracts  according  to  the  law 


we  find 

m_  i 

mo     V1 — v^_  (2) 

c2 

the  formula  given  by  relativity  for  the  transversal  mass  of  the  electron. 
If  the  electron  contracts  according  to  the  law 


a  c^ 

the  integration  yields  the  result 

HL_3    o   c2-v*   /_g_      3\       i+i    3Ml  _cVJ    (3) 

m.~8    v       v2        \c2  — v2     4/    8i— -^     i6(c2  — v2)v2 

C 

It  is  shown  that  the  first  formula  gives  values  1 3%  smaller  than 

the  experimental  values ;  the  second  formula,  that  of  relativity,  agrees 
very  well  with  the  facts ;  the  third  formula  gives  too  large  values. 


THE   VELOCITY  OF  ELECTRONS  IN  THE  PHOTO-ELECTRIC 

EFFECT,  AS  A   FUNCTION  OF  THE  WAVE 

LENGTHS  OF  THE  LIGHT 


BY  DAVID  W.  CORNELIUS 


(Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  I.,  No.  i,  Jan.,  1913.] 


THE  VELOCITY  OF  ELECTRONS  IN  THE  PHOTO-ELECTRIC 

EFFECT,    AS    A    FUNCTION    OF    THE    WAVE 

LENGTHS  OF  THE  LIGHT. 

BY  DAVID  W.  CORNELIUS. 

THE  object  of  this  investigation  is  a  determination  of  the  potential 
acquired  by  alkali  metals  when  illuminated  by  light  of  different 
wave-lengths,  and  the  determination  of  the  velocity  of  the  electrons  as 
a  function  of  the  frequency  of  the  incident  light.  Besides  the  direct 
interest  of  these  measurements,  the  importance  of  this  investigation  lies 
in  its  connection  with  the  general  theory  of  radiation  of  the  black  body 
as  developed  by  Planck  by  means  of  the  calculus  of  probability  and 
thermodynamics.  In  Planck's  theory,  which  has  been  well  confirmed 
by  the  experiments  on  the  radiation  of  the  black  body,  which  also  gives 
^ood  values  for  the  elementary  quantities  of  nature,  the  elementary 
oscillator  emits  the  radiant  energy  not  continuously,  but  intermittently 
in  definite  units  such  that  the  elementary  unit  of  radiation  energy  is  pro- 
portional to  the  frequency  of  the  light.  The  equation  is 

E  =  hn, 

where  E  is  the  energy,  n  is  the  frequency  and  h  is  a  constant  of  pro- 
portionality. On  this  theory  we  should  expect  the  positive  potential 
of  the  photo-electric  effect  to  increase  proportionally  to  n.  Some  of 
the  first  determinations  of  the  velocities  of  electrons  emitted  from  alkali 
metals  under  the  action  of  light  of  different  wave-lengths  have  been  made 
by  Jakob  Kunz,1  who  found  that  the  potentials  are  nearly  proportional 
to  the  square  of  the  frequencies  of  the  incident  light,  and  that  the  veloci- 
ties are  almost  independent  of  the  temperature  and  of  the  intensity  of 
the  light.  Two  other  recent  papers  make  further  measurements  im- 
portant. J.  R.  Wright2  finds  that  there  is  a  decided  maximum  in  the 
curve  representing  potential  and  frequency  in  the  case  of  zinc;  and  R. 
Pohl  and  P.  Pringsheim3  find  that  there  are  two  different  photo-electric 
effects  in  the  alkali  metals,  the  ordinary  and  the  selective  effect.  They 
measured,  however,  the  photo-electric  currents,  and  not  the  equilibrium 

1  J.  Kunz,  PHYS.  REV.,  Vol.  29,  3,  1909;  Vol.  31,  5,  1910. 

2  J.  R.  Wright,  PHYS.  REV.,  Vol.  33,  i,  1911. 

8  R.  Pohl  and  P.  Pringsheim,  Verhandlungen,  d.  D.  Phys.  Gesellschaft,  12,  p.  215,   1910; 
and  R.  Pohl,  Verhandlungen,  d.  D.  Phys.  Gesellschaft,  n,  715,  1909;  13,  961,  1911. 


VOL.  I.I 
No.  i.  J 


VELOCITY.   OF   ELECTRONS. 


potential  acquired  by  the  metals.  It  is  therefore  important  to  ascertain 
whether  there  are  two  different  effects  to  be  found  in  this  equilibrium 
potential,  whether  there  is  a  maximum,  or  whether  the  potential  increases 
continuously  throughout  the  range  of  the  visible  light.  Finally  the 
influence  of  the  temperature  on  the  equilibrium  potential  has  to  be 
determined. 

DESCRIPTION  OF  APPARATUS  AND  METHOD. 

The  arrangement  of  the  essential  parts  of  the  apparatus  used  in  this 
research  is  shown  in  Figs.  I  and  2.     The  source  of  light  is  a  carbon  arc  L. 


Fig.  1. 

The  light  passes  through  a  slit  and  system  of  lenses  which  gives  a  beam 
of  parallel  light  upon  the  prism  P,  which  is  capable  of  rotation,  thus 
providing  for  an  intense  source  of  light,  which  after  passing  through  the 
prism,  falls  upon  the  slit  S  of  a  light-tight  box  containing  the  photo- 
electric cell.     By  rotating  the  prism  P  any  desired  wave-length  can  be 
made  to  pass  through  the  slit  S  and  fall  upon  the  photo-electric  metal  C. 
The  illuminated  electrode  C  of  the  cell  is  connected 
through  a  key  K  and  commutator  R  to  a  pair  of         *"»irr,r 
quadrants  of  a  Dolazalek  electrometer  E.     Static  pjg  2. 

charges  were  avoided  by  having  the  cell,  connections, 
keys  and  measuring  instrument,  which  were  manipulated  from  a  distance, 
all  inside  of  earthed  conductors.  The  insulators  were  made  of  sulphur  and 
amber  plugs.  The  light  which  passes  through  the  slit  S  falls  upon  the 
metal  in  the  photo-electric  cell .  The  mirror  m  is  mounted  so  that  it  can 
be  rotated  about  the  axis  ab.  The  light  of  the  same  wave-length  as  is 
incident  upon  the  metal  is  therefore  incident  upon  the  mirror.  The 
light  is  reflected  from  the  mirror  into  a  direct  reading  spectrometer  H, 
made  by  Hilger,  which  was  calibrated  by  means  of  the  sodium  lines. 
This  proved  to  be  a  very  satisfactory  arrangement,  since  the  readings 
of  wave-length  could  be  made  as  the  rotating  prism  was  rotated  into  a 


1 8  DAVID  W.  CORNELIUS. 

desired  position.  The  suspension  of  the  electrometer  was  a  fine  quartz 
fiber  which  was  made  conducting  by  CaCl2  for  a  portion  of  the  work, 
and  a  fine  phosphor  bronze  wire  for  the  remainder.  The  deflection  of 
the  electrometer  was  read  by  the  image  of  an  incandescent  light  focused 
on  a  millimeter  scale  at  a  distance  of  about  five  meters  from  the  mirror 
of  the  electrometer  needle.  The  electrometer  was  calibrated  by  means 
of  a  standard  Weston  cell,  resistances  and  storage  battery  in  the  usual 
way.  The  calibration  of  the  electrometer  is  practically  a  straight  line. 
That  is,  the  deflections  were  proportional  to  voltage.  The  sensibility 
was  .00 1 1  volt  per  mm.  deflection.  The  electrometer  was  calibrated 
several  times  with  practically  the  same  results.  The  maximum  potential 
acquired  by  the  metal,  for  incident  light  of  any  given  wave-length, 
was  determined  by  the  deflection  of  the  electrometer.  Various  voltages 
were  used  on  the  needle  ranging  from  40  to  140,  depending  upon  the 
sensibility  desired. 

A  number  of  photo-electric  cells  were  constructed,  containing  different 
metals.  The  designs  of  the  cells  varied  considerably.  The  determina- 
tion of  the  velocity  of  electrons  emitted  from  the  surface  of  a  photo- 
electric metal  in  a  vacuum  tube,  when  acted  upon  by  light,  was  attempted 
by  different  methods.  The  stream  of  negatively  charged  electrons  will 
be  deflected  if  it  passes  through  a  magnetic  field.  The  velocity  of  the 
electrons  can  be  calculated  by  the  ratio  e/m,  where  e  is  the  charge  and  m 
the  mass  of  the  electron,  along  with  H,  the  magnetic  field  and  the  deflec- 
tion of  the  stream  of  electrons.  The  magnetic  deflection  method  was 
tried  in  several  tubes.  The  advantage  of  this  method  is  that  it  gives  an 
independent  determination  of  the  velocity  of  the  electrons,  so  that  it 
would  be  desirable  to  be  able  to  use  it.  After  repeated  trials  the  magnetic 
deflection  method  was  given  up,  since  it  was  found  impossible  to  measure 
the  photo-electric  current.  The  method  of  measuring  the  equilibrium 
potential  by  means  of  an  electrometer  is  subject  to  certain  objections 
which  could  not  be  made  against  the  deflection  method.  Any  conduc- 
tivity along  the  glass  wall  or  through  the  vapor  of  the  alkali  metal 
diminishes  the  final  value  of  the  equilibrium  potential.  Moreover  the 
potential  measured  by  the  electrometer  is  due  to  the  equilibrium  potential 
and  partly  to  contact  electro-motive  forces  or  potential  differences  of 
any  other  nature.  All  those  influences  could  at  once  be  avoided  by  the 
magnetic  deflection  method. 

Several  cells,  which  are  not  shown  in  a  diagram,  were  unsuccessful. 
Two  rubidium  cells  showed  some  interesting  features.  Exposed  to  light 
they  showed  in  the  beginning  considerable  sensitiveness,  which  decayed 
rapidly  until  they  did  not  respond  even  to  intense  light.  After  being  left 


NS"i!']  VELOCITY   OF  ELECTRONS.  19 

in  the  dark  for  a  short  time,  they  would  sometimes  recover.  The  photo- 
electric metal  was  melted  several  times,  but  apparently  was  not  effective 
in  changing  the  behavior  of  the  cells.  The  same  behavior  was  observed 
in  a  potassium  cell.  It  was  put  in  sunlight  for  several  hours,  but  this  did 
not  result  in  the  cell  becoming  consistently  active.  This  phenomenon 
might  be  called  a  fatigue,  the  cause  and  character  of  it  are  still  uncertain. 
Thus  we  see  that  this  work  is  attended  with  many  difficulties.  There  are 
a  number  of  sources  of  error.  A  small  leak  in  the  tube,  a  slight  impurity 
of  the  photo-electric  metal,  and  its  surface  conditions,  gas  developed  in 
the  tube  due  to  wax  joints  or  occluded  gas  in  the  metals  in  the  tube, 
static  charges  on  the  glass  of  the  tube,  imperfect  insulation  between  the 
electrodes  of  the  cell,  enter  as  factors,  rendering  this  experimental  work 
difficult  of  execution.  In  several  experiments  it  has  been  observed  that 
the  photo-electric  metal  in  the  dark  chamber  acquired  spontaneously  a 
negative  potential,  which  developed  very  slowly  and  arose  to  quite 
considerable  values.  This  effect  has  since  been  studied  by  J.  W.  Wood- 


Fig.  3.  Fig.  4. 

row.  In  those  cells  which  gave  the  best  and  most  consistent  results  this 
negative  effect  has  not  been  observed.  If  it  existed  it  must  have  been 
so  slow  that  it  could  not  effect  the  readings  to  any  measurable  amount. 

The  general  type  of  cell  which  has  proved  to  be  the  most  satisfactory 
in  this  investigation  is  shown  in  Figs.  3  and  4.  The  metals  used  were 
potassium,  potassium  "fixed"  with  hydrogen,  caesium,  and  caesium 
"fixed"  with  hydrogen.  There  were  only  slight  variations  of  the  design 
of  the  cell  to  suit  the  introduction  of  the  different  metals,  or  conditions 
desired  for  the  cell. 

Csesium  was  prepared  for  introduction  into  the  cell,  by  first  drying 
caesium  chloride  by  melting  it  in  contact  with  dry  hydrochloric  acid  gas. 
Fourteen  grams  of  dry  caesium  chloride  were  mixed  with  2.5  grams 
calcium,  placed  in  an  iron  boat  in  a  combustion  tube  of  Bohemian  glass. 
When  the  temperature  rises  the  reaction  beween  the  Ca  and  the  CsCl, 
or  RbCl,  becomes  quite  violent  and  the  calcium  and  the  salts  spread 
out  and  condense  together  with  the  rubidium,  or  caesium,  in  the  cooler 
parts  of  the  combustion  tube.  To  prevent  this  mixture,  a  plug  of 


2O  DAVID  W.  CORNELIUS. 

asbestos  and  iron  wire  keep  the  iron  boat  in  position  and  allow  the 
rubidium,  or  caesium,  vapor  alone  to  pass  through  the  plug.  The  com- 
bustion tube  is  connected  by  means  of  sealing  wax  and  glass  tubes  to  the 
photo-electric  cell.  After  the  tube  was  exhausted  the  combustion  tube 
was  heated  gradually  until  the  metal  distilled  and  ran  through  the 
connecting  tubes  into  the  cell.  Rubidium  and  caesium  were  both  pre- 
pared in  the  same  manner.  Potassium  was  introduced  into  the  bulb 
M,  of  Figs.  3  and  4,  distilled  into  K  and  poured  into  C.  The  cells 
were  all  exhausted  by  a  Gaede  pump.  The  vacuum  in  each  case  was 
tested  by  the  characteristics  of  the  discharge,  from  an  induction  coil 
between  two  electrodes  in  the  system.  A  flame  was  kept  under  the 
charcoal  bulb  for  several  hours  until  the  charcoal  ceased  to  develop 
•gas  and  the  pump  was  able  to  exhaust  the  system  to  a  stage  of  hard 
Roentgen  rays.  If  the  metal  introduced  was  to  be  left  in  the  pure  state 
without  hydrogen,  the  tube  was  sealed  off  from  the  pump  as  soon  as  the 
metal  was  distilled  and  transferred  into  the  final  position.  However,  if 
ihe  metal  was  to  be  "fixed"  with  the  hydrogen,  the  cell  was  not  sealed 
T)ff  from  the  pump  until  later.  The  hydrogen  was  introduced  by  means 
of  palladium,  Pd,  of  Figs.  3  and  4.  This  metal  was  used  as  a  cathode  in  a 
solution  of  three  parts  water,  and  one  part  H2SO4  When  the  electric 
current  passes  through  this  cell  the  Pd  absorbs  a  large  amount  of  hydrogen 
which  is  given  off  again  by  gently  heating  the  dry  metal  with  a  bunsen 
flame,  in  Pd  of  Figs.  3  and  4.  When  the  cell  contains  a  small  amount  of 
hydrogen  and  a  discharge  passes  from  the  alkali  metal  to  the  anode  the 
surface  of  the  alkali  metal  assumes  very  intense  colors,  due  to  the  com- 
bination of  the  metal  with  hydrogen  or  else  to  a  colloidal  transformation 
of  the  metal.  This  process  we  may  call  fixing  or 
forming.  In  this  forming  the  potassium  assumes 
intense  blue  or  purple  colors,  while  the  caesium  ex- 
hibits a  greenish  gray  or  bronze  surface. 

A  caesium  cell  No.  10  without  charcoal  bulb  is 
shown  in  Fig.  5.     Caesium  is  distilled  into  the  bulb  at 
C  when  the  electrode  A  is  raised,  by   means  of  a 
p.     -  magnet,  in  order  that  no   caesium  vapor  condense 

upon  the  electrode.  The  diameter  of  the  bulb  is 
about  5  cm.,  and  the  distance  between  A  and  C  about  2  cm.  The  data 
for  this  cell  are  given  in  Table  I. 

The  curve  of  Table  I.  is  quite  similar  to  that  obtained  by  Jakob  Kunz1 
under  similar  circumstances.  The  cells  which  he  used  did  not  have  any 
charcoal  bulbs  attached.  Thus  it  will  be  noted  that  this  cell  which  does 

*J.  Kunz,  PHYS.  REV.,  Vol.  29,  3,  1909. 


VOL.  I. 
No.  i. 


VELOCITY   OF  ELECTRONS. 


not  have  charcoal  bulb  attached  verifies  his  work.  The  variations  of  this 
curve  from  a  smooth  curve  is  in  a  measure  due  to  residual  pressure  in  the 
cell.  This  error  is  reduced  almost  entirely  where  charcoal  and  liquid  air 
are  used. 

TABLE  I. 

Cesium  Cell  No.  10.     t  =  23°  C. 


Wave-length. 

X 
MM 

Frequency2. 

JV* 
I0*> 

Volts. 

V 

Wave-length. 

MM 

Frequency2. 

TV2 

I0*> 

Volts. 

V. 

420 

.510 

1.168 

570 

.278 

0.606 

450 

.444 

1.090 

600 

.250 

0.517 

480 

.391 

1.010 

630 

.227 

0.387 

510 

.346 

0.920 

660 

.207 

0.343 

540 

.309 

0.748 

690 

.189 

0.325 

Volts  on  needle  of  electrometer  126. 


=  .001202. 


Caesium  cell  No.  12  was  similar  to  Fig.  3.     The  metal  was  distilled 
upon  an  iron  plate  at  B  of  Fig.  3  and  moved  by  means  of  a  magnet  to  a 

final  position  C.  A  is  an  alu- 
minium plate  1X3  cm.  The 
distance  between  electrodes  was 
about  4  mm.  The  tube  was  2 
cm.  in  diameter  and  18  cm. 
long.  The  caesium  was  not 
"fixed  "  with  hydrogen  before  the 
cell  was  sealed  from  the  pump, 
The  cell  was  first  tried  with  the 


03 
02 
0.1 

a 

JH 


WVL  LENGTHS 


42.       4<> 


Fig.  6. 


metal  pure,  but  was  found  not  to- 
be  photo-electric.  After  three 
days'  effort  it  was  decided  to 
"fix"  the  metal.  It  was  done  in  the  usual  manner.  However,  since 
the  cell  had  been  previously  sealed  from  the  pump,  the  residual  hydro- 
gen in  the  tube  was  not  pumped  out  after  fixing,  but  left  for  the  char- 
coal to  absorb  when  immersed  in  liquid  air.  The  results  of  this  cell  are 
given  in  Fig.  6.  Liquid  air  was  kept  on  the  charcoal  bulb  continuously 
during  the  series  of  observations.  The  time  elapsing  between  the  read- 
ings for  curves  1-4  was  about  43  hours. 

The  characteristics  of  the  curves  change  gradually  with  time.  This  is 
due  probably  to  the  absorption  of  the  residual  hydrogen,  by  the  charcoal. 
The  change  seems  to  indicate  that  the  curves  are  approaching  a  form 
such  as  would  finally  make  the  maximum  potential  proportional  to  the 
square  of  the  frequency.  It  was  impossible  to  keep  liquid  air  on  the  cell 


22 


DAVID  W.  CORNELIUS. 


[SECOND 

[SERIES. 


continuously,  and  make  observations  until  such  a  steady  state  was 
reached.  It  is  probable,  moreover,  that  the  surface  of  the  metal  under- 
goes slight  changes  so  that  the 
sensitiveness  either  increases  or 
decreases  in  the  course  of  time. 

Potassium  was  placed  in  bulb 
M,  Fig.  4,  distilled  into  K  and 
poured  through  funnel  F  into 
final  position  C  in  cell  No.  4. 
The  surface  of  the  potassium  be- 
came darkened  to  a  reddish  pur- 
ple color,  as  the  cell  was  left  ex- 


UWE  LENGTHS 


,54  60 

Fig.  7. 


posed  to  the  light  of  the  room 
for  six  days  before  the  observa- 
tions, shown  in  Table  II.  and  curves  of  Figs.  7  and  8  were  taken. 

TABLE  II. 

Cesium  Cell  No.  4.     t  =  23°  C. 


Wave-length. 
MM 

Frequency2. 

A2 
1080 

Volts. 

V 

Wave-length. 
MM 

Frequency2. 

A'2 
I030 

Volts. 

"V 

420 

.510 

1.070 

600 

.250 

0.394 

450 

.444 

0.890 

630 

.227 

0.356 

480 

.391 

0.730 

660 

.207 

0.335 

510 

.346 

0.609 

690 

.189 

0.279 

540 

.309 

0.523 

720 

.173 

0.249 

570 

.278 

0.472 

750 

.160 

0.243 

Qft 


Volts  on  needle  of  electrometer- 12 7.     Km  =  .00150. 

These  curves  are  very  significant.  The  curve  of  Fig.  7  certainly  is  not 
a  straight  line  as  Planck's  law 
would  require,  but  Fig.  8 
shows  a  straight  line  within  a 
reasonable  error  of  observa- 
tion. There  is  a  slight  varia- 
tion in  the  points  near  the  red 
end  of  the  spectrum,  but  that 
is  probably  due  to  the  great 
difficulty  of  determining  those 
points  accurately.  It  was 
found  that  the  maximum 
equilibrium  potential  was  in- 
dependent of  the  intensity  of  the  incident  light,  within  the  limits  of  the 


FREQUENCY 


22 


0         J4 

Fig.  8. 


VOL.  I.] 
No.  i.  J 


VELOCITY   OF  ELECTRONS. 


full  intensity  due  to   the  arc,  and  the  intensity  of  the  light  due  to  an 
incandescent  lamp  directed  upon  the  cell. 

Cell  No.  8  was  a  cell  in  which  the  active  metal  was  potassium  fixed 
with  hydrogen.  It  was  similar  to  Fig.  3.  The  potassium  was  dis- 
tilled upon  a  platinum  plate  (which  had  iron  attached)  at  position 
B,  Fig.  3,  and  moved  into  position  C  by  means  of  a  magnet.  The 
electrode  distance  was  about  2  mm.  The  potassium  was  fixed  in  the 
usual  manner,  as  described  before,  but  was  not  photo-electric.  The 
movable  electrode  was  moved  back  to  position  B  and  the  potassium 


WAVELENGTHS 


34- 


60 


Fig.  9. 


50 


melted.  When  the  electrode  was  removed  back  to  position  C,  it  was 
photo-electric.  Observations  were  made  upon  the  cell  for  three  consecu- 
tive days,  which  indicated  a  positive  potential  of  the  alkali  metal  when 
exposed  to  light.  The  potential  was  erratic  however.  Nine  days  later 
consistent  observations  were  made  upon  the  cell  as  shown  in  data  of 
Table  III.,  and  Figs.  9  and  10. 

TABLE  III. 

CcBsium  Cell  No.  8.     t  =  23°  C. 


Wave-length. 

MM 

Frequency8. 

N*    • 

1030 

Volts. 

•v 

Wave-length. 

MM 

Frequency2. 

N* 

Volts. 

V 

420 

.510 

.835 

570 

.278 

.407 

450 

.444 

.722 

600 

.250 

.361 

480 

.391 

.622 

630 

.227 

.348 

510 

.346 

.537 

660 

.207 

.326 

540 

.309 

.488 

690 

.189 

.266 

Volts  on  needle  of  electrometer  106.     Km  =  .00141. 

These  plates  show  the  same  characteristic  properties  of  the  phenome- 
non.    The  equilibrium  potential  is  proportional  to  the  square  of  the 


DAVID  W.  CORNELIUS. 


[SECOND 

L  SERIES. 


frequency.     This  is  always  the  case  when  the  metal  is  in  the  permanent 
state  of  activity. 

Caesium  was  poured  into  position  C  in  cell  No.  13,  which  was  of  the 
form  shown  in  Fig.  4.  The  surface  was  "fixed"  in  the  usual  manner. 
The  color  of  the  surface  was  a  greenish  gray  and  partly  bronze.  When 


WAVL  LENGTHS 


WftV£  LENGTHS 


Fig.  11. 


54  60 

Fig.  12. 


72- 


liquid  air  was  applied  to  the  charcoal  bulb,  the  metal  was  not  active  in 
the  beginning.  Violet  light  was  incident  upon  the  cell  for  an  hour,  or 
more,  before  the  electrometer  indicated  a  positive  deflection  of  510  mm. 
which  is  equivalent  to  .062  volt.  A  set  of  observations  was  taken,  as 
recorded  in  curve  I  of  Fig.  n.  The  maximum  potential  was  reached 

very  quickly  after  the  metal 
was  connected  to  the  electrom- 
eter, but  was  very  difficult  to 
read  accurately.  Liquid  air 
was  kept  continuously  on  the 

0.31-          ^      ^^  ^  bulb  and  a  series  of  observa- 

tions was  taken  about  twelve 
hours  later,  as  recorded  in  curve 
3,  Fig.  II.  About  nine  hours 
later  another  series  was  taken 
as  shown  in  curve  3  of  the  same 
figure.  The  cell  was  left  un- 
disturbed for  four  days  (due  to  a  lack  of  liquid  air).  After  this  time 
another  series  of  observations  was  taken  upon  the  cell  as  given  in  Table 
IV.  and  curve  I  of  Figs.  12  and  13.  (The  time  required  for  the  completion 
of  a  series  is  about  two  hours.)  Then  following  this  series  another  was 
immediately  taken,  Table  IV.  and  curve  2,  Figs.  12  and  13.  The  cell 
was  placed  in  an  ice  bath  and  another  set  of  observations  for  o°  C.  was 
taken  which  is  recorded  in  Table  IV.  and  curve  3  of  Figs.  12  and  13.  Two 


VOL.  I. 
No.  i. 


VELOCITY   OF   ELECTRONS. 


days  later  sets  of  data  were  taken  for  variation  in  temperature  as  shown 
in  Table  V. 

TABLE  IV. 

Casium  Cell  13.     4  days  later  than  Fig.  11. 
X  =  wave-length.     N2  =  frequency2,     v  =  volts. 


\ 

N* 

Time,  3  P.  M. 
Tern.,  23°  C. 

V 

Time,  6  P.  M. 
Tern.,  23°  C. 

•v 

Time,  10  P.  M. 
Tern.,  o°  C. 

v 

420 

.510 

.468 

.414 

.604 

450 

.444 

.392 

.373 

.520 

480 

.391 

.355 

.368 

.470 

510 

.346 

.301 

.342 

.420 

540 

.309 

.259 

.305 

.382 

570 

.278 

.220 

.272 

.345 

600 

.250 

.197 

.249 

.306 

630 

.227 

.168 

.228 

.288 

660 

.207 

.145 

.220 

.248 

690 

.189 

.132 

.204 

.204 

Volts  on  needle  of  electrometer  127.     K\yj  =  .00120. 

TABLE  V. 

Casium  Cell  13.     2  days  later  than  Figs.  12  and  13. 
X  =  wave-length.     N2  =  frequency2,     v  =  volts. 


A 

N* 

Tern.,  23°  C. 

v 

Tem.,40°C.(?) 

V 

Tern.,  o°  C. 

v 

420 

.510 

.475 

.600 

1 

450 

.444 

.405 

.528 

l 

480 

.391 

.378 

.486 

.483 

510 

.346 

.348 

.450 

.455 

540 

.309 

.318 

.414 

.420 

570 

.278 

.288 

.367 

.374 

600 

.250 

.258 

.342 

.348 

630 

.227 

.242 

.294 

.298 

660 

.207 

.228 

.248 

.256 

690 

.189 

.205 

.212 

.214 

Volts  on  needle  of  electrometer  127.     Km  =  .00120. 

The  curves  of  Fig.  n  indicate  a  change  with  time  similar  to  Fig.  6. 
There  seems  to  be  a  growth  in  the  sensibility  of  the  cell  as  well  as  a 
smoothing  of  the  curves.  The  surface  of  the  photo-electric  metal  seems 
to  undergo  a  change  until  it  finally  reaches  a  steady  state,  in  which  the 
maximum  potential  varies  as  the  square  of  the  frequency  of  the  incident 
light. 

1  Reading  of  the  electrometer  uncertain.  Possibly  rise  of  the  temperature  of  the  cell, 
poor  insulation,  and  negative  effect  are  the  causes  of  the  difficulty.  The  cell,  in  this  case, 
became  negative  in  a  very  few  minutes  when  in  the  dark. 


26  DAVID  W.  CORNELIUS.  HEWES! 

The  set  of  curves  I  and  2,  in  Figs.  12  and  13,  shows  the  cell  to  have 
reached  a  steady  state.  It  is  interesting  to  note  the  development  of  the 
cell.  There  is  some  suspicion  to  believe  that  the  sensibility  increases 
within  the  length  of  time  (two  hours)  required  to  make  a  set  of  observa- 
tions. Curve  2  is  read  from  the  red  to  the  violet  end  of  the  spectrum. 
Curve  3  for  ice  temperature  is  a  little  uncertain  at  the  end  points,  the 
electrometer  being  difficult  to  read  in  that  region.  All  the  errors,  im- 
perfect insulation,  rise  of  temperature  of  the  cell,  etc.,  tend  to  lower  the 
points.  There  is  a  little  uncertainty,  therefore,  as  to  the  character  of 
curve  3,  since  the  shifting  of  a  few  of  the  end  points  may  be  critical  in 
determining  the  form  of  the  curve. 

GENERAL  RESULTS. 

Let  us  consider  the  significance  of  this  experimental  work.  We  see  that 
Planck's  law,  which  states  that  the  maximum  potential  acquired  by  the 
alkali  metal  should  be  proportional  to  the  frequency  of  the  incident  light, 
is  not  corroborated.  But,  on  the  other  hand,  the  maximum  equilibrium 
potential  of  the  metal  P  varies  as  the  square  of  the  frequency  n  of  the 
light.  This  relation  is  expressed  by  the  equation, 

P  =  kn*  +  Po, 

where  k  is  a  factor  of  proportionality  and  Po  a  constant.  The  theory,  as 
developed  by  J.  Kunz,1  is  expressed  in  the  form  E  =  kri*,  where  E  is  the 
energy  of  the  vibrating  Faraday  tube  in  the  beam  of  light,  k  is  a  factor 
of  proportionality  and  n  the  frequency  of  the  light.  If  light  falls  upon 
a  photo-electric  metal  a  part  of  the  energy  is  reflected  and  a  part  absorbed, 
both  being  proportional  to  the  square  of  the  frequency.  In  order  that  an 
electron  may  escape  from  the  metal,  its  kinetic  energy  must  be  sufficient 
to  overcome  the  attraction  of  the  positive  charge  left  behind.  An  elec- 
tron, in  passing  through  the  metal,  may  lose  some  energy  by  collision 
with  molecules  of  the  metal  before  it  reaches  the  surface.  Let  us  call 
this  loss  of  kinetic  energy  w.  Then  the  electron  leaves  the  surface  of  the 
metal  with  a  kinetic  energy  E  =  kn2  —  w.  The  metal  acquires  a  positive 
charge  and  a  maximum  potential  of  P,  when  the  electrons  are  escaping, 
which  is  in  equilibrium  with  the  energy  of  the  escaping  electrons.  If  the 
charge  of  an  electron  is  e,  then  Pe  =  akn2  —  w.  We  are  able  to  calculate 
the  values  for  the  constant  w,  from  the  experimental  observations.  The 
straight  lines  of  Figs.  8,  10  and  13,  which  represent  the  relation  of  maxi- 
mum potential  and  square  of  frequency,  may  be  expressed  in  the  form 

P  =  sri*  +  w. 
1  J.  Kunz,  PHYS.  REV.,  Vol.  29,  3,  1909. 


VOL.  I.I 
No.  i.  J 


VELOCITY   OF   ELECTRONS. 


If  P  =  o,  then  sn2  =  w.  Thus  graphically  w  is  the  point  where  the 
curve  crosses  the  y  axis,  if  P  =  y  and  x  =  n2.  Several  values  have 
been  calculated  from  the  data  which  are  given  in  the  table  below.  The 
method  of  calculation  may  be  made  clear  by  a  sample  calculation  taken 
from  Fig.  13, 

Pi  -P. 

5    = 


where  PI  is  potential  in  absolute  units  for  a  frequency  »i,  and  P2  is  the 
potential  in  absolute  units  for  a  frequency  nz.     This  gives 

Pi  -  P2 
*  «        — X  300, 


where  P\  and  PI  are  expressed  in  volts. 

(.468  -  .132) 


s  = 


300  X  .51  X  io30  -  :i8  X  io30      * 


X  io-32 


for  the  slope  of  curve  I,  Fig.  13.  Applying  this  value  in  the  formula  for 
the  case  where  X  =  420^ 

w  =  Pl  -  sn?  =  .468  -  (.34  X  io-32  X  .51  X  io30  X  300) 

=  —  .052  volt  =  .174  X  io~4  abs. 
e  X  w  =  4.65  X  io-10  X  174  X  io-4  =  -  .0807  -io-12  ergs. 

This  represents  the  energy  lost  by  the  electron  in  reaching  the  surface 
or  the  amount  of  work  necessary  to  drag  an  electron  to  the  surface  of  the 
metal. 

VALUE  OF  WORK  TO  BRING  ELECTRON  TO  SURFACE. 
TABLE  VI. 


Metal  in  Cell. 

Caesium 
23°  C. 

Caesium 
o°  C. 

Caesium  23° 
C.,  48  Hrs. 
Later. 

Pot.  Cell 
No.  i. 

Pot  Cell 
No.  8  with  H. 

Values  of  5  X  10~32. 

.340 

.368 

.273 

.817 

.574 

.344 

.376 

.273 

.827 

.575 

.338 

.369 

.272 

.822 

.563 

.346 

.370 

.277 

.833 

.573 

.340 

.369 

.270 

.847 

.575 

Mean  5  X  10~32.  .  . 

.342 

.374 

.273 

.829 

.572 

Work  in  volts  

—  .052 

+.037 

+.057 

-  .160 

-.041 

Work  inergsXlQ-13 

-.807 

+.572 

+.888 

-2.480 

-.667 

The  velocity  of  an  electron  emitted  from  the  surface  is  given  by  the 
equilibrium  relation  Pe  =  ]^>mv2,  where  P  is  the  maximum  potential,  e 


28 


DAVID  W.  CORNELIUS. 


[SECOND 

[SERIES. 


the  charge  of  the  electron,  m  its  mass  and  v  its  initial  velocity  of  emission 
from  the  surface.     Hence 


m 

gives  the  formula  for  the  calculation  of  the  velocity  where  e/m  is  1.77  X  io7 
and  P  has  values  as  determined  by  observations. 

VALUES  OF  INITIAL  VELOCITY  OF  ELECTRONS. 
TABLE  VII. 


Cell. 

A  in  nn. 

PAbs.  Units. 

v=    t^p,  ™. 

\     m     '  sec 

Pot.  No.  4 

420 

1.09  X  IO8 

6.21  X  IO7 

Pot.  No.  4  

690 

.266  X  IO8 

0.97  X  IO7 

Pot.  No.  4  
Pot.  No.  8  

750 
420 

.233  X  IO8 
.835  X  IO8 

0.91  X  IO7 
5.45  X  IO7 

Pot.  No.  8  
Caesium  No.  13  with  H 
Caesium  at  23°  C. 

690 
420 
690 

.266  X  IO8 
.472  X  IO8 
.780  X  IO8 

0.97  X  IO7 
4.09  X  IO7 
0.78  X  IO7 

At  ice 

420 

600  X  IO8 

4.61  X  IO7 

At  0°  C  

690 

.177  X  IO8 

0.79  X  IO7 

Planck's  law  as  expressed  by  the  equation, 


E  =  hn  = 


which  may  be  written 


+  C, 


hn  =  Pe  +  C, 


gives  the  right  order  of  magnitude  for  the  velocity  of  the  electron  although 
it  does  not  express  the  relation  of  the  velocity  of  the  electrons  as  a  function 
of  the  frequency  of  the  incident  light,  h  has  a  value  of  6.548  X  io~27 
ergs  sec.  The  velocity  is  given  by  the  equation  (i)  v  =  1/2/m/w.  For 
light  of  wave-length  420^  n  =  0.715-  io15.  The  mass  of  the  electron  is 
8.7  X  io~28  grams.  These  values  applied  to  the  formula  give 


\2hn 

==  W  ^  = 


2  X  6.55  X  io-27X7i5 


=  I0'3  x  I0  cm*  sec* 


This  compares  well  with  the  experimental  values.  However,  the 
experimental  values  for  the  maximum  potential  acquired  by  the  metal, 
for  light  of  different  frequencies,  are  different  from  those  calculated  by 
means  of  the  equation  of  Planck, 

hn  =  Pe  +  C, 
where  h  is  6.5  X  io~27,  e  is  4.65  X  icr10  and  C  is  2.4  X  io~12.     This  varia- 


VOL.  I.I 
No.  i.  J 


VELOCITY   OF  ELECTRONS. 


29 


tion  of  the  experimental  results  from  Planck's  law  is  made  clear  by  a  set 
of  calculations  for  potassium  cell  No.  8,  which  is  shown  in  Table  VIII. 

TABLE  VIII. 


« 

I0« 

Potential  r,  Calculated 
by  Planck's  Law,  Volts. 

Potential  Observed  F8. 

Difference  Fj  —  F2  Volts. 

.435 

.266 

.266 

.455 

.354 

.326 

.028 

.476 

.438 

.348 

.090 

.500 

.541 

.361 

.180 

.527 

.654 

.407 

.247 

.556 

.781 

.488 

.293 

.588 

.909 

.537 

.372 

.625 

1.063 

.622 

.441 

.666 

1.242 

.722 

.520 

.714 

1.440 

.835 

.605 

The  work  done  in  expelling  an  electron  can  be  computed.  The  work 
done  in  moving  an  electron  of  charge  e\  (which  must  be  equal  to  e%  or  a 
multiple  of  e%)  through  a  distance  dr  is 

r  dr 


dw  =  72" dr' 

The  work  done  in  moving  the  electron  to  infinity  (i.  6.,  beyond  the  field 
of  attraction  of  the  atom)  is : 

-  CO 

dr  6162  e\62 

7=        r        =  ~R' 


w 


where  R  is  the  radius  of  the  atom.     Now 


w 


~- 


Hence 


J2  6162 
iRm* 


This  is  the  velocity  necessary  that  the  electron  may  escape  from  the 
metal. 

If  an  electron  revolves  about  the  positive  atom  it  has  kinetic  energy 
due  to  its  rotation.  The  velocity  of  the  electron  is  determined  by 
the  equilibrium  of  the  centrifugal  and  centripetal  forces.  If  the  electron 
has  a  mass  w2,  a  charge  e2,  linear  velocity  v  and  the  positive  atom  has  a 


3O  DAVID  W.  CORNELIUS. 

mass  mi,  charge  e\  (which  must  equal  e^  or  a  multiple  of  e2)  and  a  radius 
R-,  then 

I   W2fl2  I  6162 

2~R~    =  2  R2  ' 

if  the  revolution  is  in  a  circle,  which  is  the  case  when  mi  is  large  as  com- 
pared to  w2.     This  gives 

T^T^ 
K.E.  = 


F.  A.  Lindemann1  has  used  this  formula  in  his  determination  of  the 
wave-length  for  which  the  selective  photo-electric  current  reaches  a 
maximum.  Thus  the  work  that  has  to  be  communicated  to  the  electron 
by  the  incident  light  is  the  difference  between  the  total  work  done  in  the 
expulsion  of  an  electron  and  its  energy  due  to  rotation,  viz., 

1*14 

,,-K.E.-^. 

The  values  of  the  velocity,  computed  by  this  deduction,  are  near  the 
values  found  by  experiment.     Suppose  that 

e\  —  charge  of  the  atom  =  ez  =  4.65  X  io~10 

,J  =  5.35x10". 

Rk  —  radius   of  potassium  atom  =  2.37  X  icr8  cm.  used  by  Linde- 
mann.2 


2  X  4-65  X  IP"10  X  5-35  X  io17  7  cm. 

2.37  X  to-  -=4.58Xio'  — 

=  velocity  of  the  electron  from  potassium  atom. 
The  atomic  volumes  vary  as  the  cubes  of  the  atomic  radii,  so  we  have 


which  determines  the  value  of  Rc»whenRk  is  known.     RC8  =  2.75  X  io~8cm. 
Then 


2  X  4-65  X  I0"10  X  5-35  X  IQl7  7  cm- 

2.75  X  io-8  )  sec. 

=  velocity  of  electron  from  caesium  in  order  that  it  may  escape. 

1  F.  A.  Lindemann,  Verh.  der  Deutschen  Phys.  Gesell.,  13,  No.  12,  1911. 
2F.  A.  Lindemann,  Verh.  Deutschen  Phys.  Gesell.,  13,  No.  12,  1911. 


'i!']  VELOCITY    OF  ELECTRONS.  31 

By  means  of  the  formula, 


the  work  necessary  to  expel  an  electron  from  the  metal  can  be  computed. 
Using  values  as  in  the  above  calculation,  we  get  for  the  work  which  needs 
to  be  supplied  by  the  incident  light  to  expel  an  electron,  in  case  of 
potassium, 

1  44       I  (4.65  X  io-10)2 

w  -  K.E.  «-—•*.-  —  —  =  4.57  X  io~12  ergs. 

2  R        2    2.47  X  icr8 

For  caesium, 

v  _  K.E.  .  K4.65X,o-y  m 

2     2.75   X   IO-8 

The  electron  theory  gives  a  means  of  calculating  the  time  required  for 
an  electron  to  be  emitted  photo-electrically.  The  differential  equation 
for  the  condition  of  resonance  of  the  electron,  when  acted  upon  by  an 
electrical  wave,  due  to  the  vibration  of  the  incident  light,  is 

d?xdx          ,    dx       2e2/d2x\2  dx 

mdt*dt+aXJt+3c(d?)     =£°cos^' 

This  may  be  written 

dE       2e2/d2x2  dx 


E  is  the  energy  of  the  vibrating  electron,  e  its  charge,  C  the  velocity  of 
light,  EQ  the  amplitude  of  the  electric  force  in  the  light  vector,  times  e, 
$  the  frequency  =  2-rrn,  and  x  the  displacement  from  the  position  of 
equilibrium.  A  particular  solution  gives  x  =  h  cos  (<f>t  —  a). 


dx  2  e 

=    -A*  sin    #-«,     ta  = 


h  = 


where  00  is  the  frequency  of  the  applied  electrical  force  and  <j>  is  the 
frequency  of  the  electron's  vibrations.  Introducing  these  values  in  the 
equation  (i)[gives 

2  e2  I  d2x    2  E02(f>  cos  </>/  sin  (<£/  —  a)dt 


32  DAVID  W.  CORNELIUS.  [lS?Bs! 

If  the  electron  is  considered  to  have  a  unit  charge  then  the  work  done  in 
one  revolution,  in  time  T,  is 


cos      sin    &  ~~ 


/*r 

To  integrate  I     cos  0/  (sin  <j>t  cos  a  —  cos  <f>t  sin  a)  <&,  put  <j>t     =    x, 
Jo 

<£d/  =  dx,  dt  =  dx/4>.     Then  the  integral  becomes  —  sin  a-T/2. 
Hence, 


Since  </>T  =  2-rr, 

EC?  sin 


is  the  work  done  in  one  revolution  or  complete  vibration  of  the  light 
vector  considering  the  moving  charge  as  unity.  If  the  electron  is  in 
resonance  with  the  light  vector,  then  $0  =  <j>  and  a  =  ir/2.  Hence, 


(    sn  air 
E    =   ~~         becomes 


2 


If  the  charge  of  the  electron  be  taken  as  e  instead  of  unity,  as  in  the  above 
consideration,  the  work  dw  done  by  the  electric  force  £0  is 

dw  =  E0edx. 
Therefore, 

27r        3  £02X3 


2ecm2       g  16      7T2 

3    C 

The  values  for  £0  =  0.003  E.S.U.  (estimated)  and  X  =  420^  =  4.2 
X  io~5  cm.,  when  substituted  in  the  above  equation,  give 


This  is  the  work  supplied  to  the  electron  by  one  vibration  of  the  light 
vector.     It  was  found  by  means  of  the  previous  deduction  that  the  work 


VELOCITY   OF  ELECTRONS.  33 

necessary  to  liberate  an  electron  is  4.2  X  io~12  ergs.     Thus  we  get  the 
number  of  vibrations  necessary  to  liberate  an  electron  which  is 


4.2  X  io-l: 

1.3  X  10 


_20  =  3  X  10*. 


Therefore,  the  length  of  time  to  liberate  an  electron  is  that  required 
for  3  X  io8  vibrations  of  the  light  vector.  For  X  =  420^,  the  time  is 

X       4.2  X  io-5 
/  =  C=     3  X  io"      =  MX  io- sec. 

Hence  the  time  for  3  X  io8  vibrations  is  3.1  o8  X  1.4  X  io~15  =  4.2  X  io~7 
second. 

Thus  the  time  required  for  the  liberation  of  an  electron  from  a  molecule 
by  the  incident  light  is  very  small.  A  conception  of  this  period  of  time, 
however,  can  be  obtained  in  terms  of  the  distance,  traversed  by  light 
in  this  interval,  which  is  3  X  io10  X  4  X  io~7  =  120  meters. 

SUMMARY. 

The  principal  results  of  this  investigation  are  as  follows: 

1.  A  small  amount  of  residual  gas  in  the  photo-electric  cell  influences 
its  behavior. 

2.  The  surface  conditions  of  the  alkali  metal  has  a  very  large  influence 
upon  the  photo-electric  effect;  which  may  be  constant  from  the  beginning 
or  increase  or  decrease  in  the  course  of  time. 

3.  It  takes,  as  a  rule,  some  time  for  a  cell  to  reach  a  steady  state  of 
sensibility. 

4.  The  attempts  to  measure  the  velocities  of  the  electrons  by  means  of 
the  magnetic  deflection  have  been  unsuccessful. 

5.  The  results  obtained  indicate  that  the  equilibrium  potential  depends 
to  some  extent  upon  the  temperature  of  the  metal,  above  zero  degrees; 
below  zero  degrees  the  equilibrium  potential  seems  to  be  independent  of 
the  temperature.     Further  experiments  upon  this  point  are  necessary. 

6.  The  relation  of  the  velocity  of  the  electrons  and  the  frequency  of 
the  incident  light  is  the  same  for:  pure  potassium,  potassium  "fixed" 
with  hydrogen,  caesium  and  caesium  "fixed"  with  hydrogen.     And  the 
relation  between  the  equilibrium  potential  and  the  frequency  of  the 
incident  light  is  the  more  constant  the  nearer  the  metal  approaches  the 
permanent  state  of  sensitiveness. 

7.  The  theoretical  and  calculated  values  of  the  initial  velocity  of  the 
electrons  are  both  of  the  order  of  io7  cm.  per  second. 

8.  The  theoretical  value  of  the  time  required  for  the  expulsion  of  an 


34  DAVID  W.  CORNELIUS. 

electron  due  to  the  resonance  effect  of  the  incident  light  is  of  the  order 
of  io~7  second. 

9.  The  equilibrium  potential  of  the  electrons  in  the  photo-electric 
effect  varies  directly  as  the  square  of  the  frequency  of  the  incident  light. 
Planck's  law,  according  to  which  the  units  of  the  electromagnetic  energy 
are  proportional  to  the  frequency  is  not  confirmed  by  the  results  of  this 
investigation. 

10.  While  the  theory  of  resonance  shows  that  a  beam  of  light  may 
supply  a  sufficient  amount  of  energy  for  the  electron  to  escape  it  cannot 
satisfactorily  account  for  the  essential  fact  that  the  velocity  of  the  elec- 
trons escaping  from  the  metal  is  proportional  to  the  frequency. 

The  author  takes  great  pleasure  in  acknowledging  his  indebtedness  to 
Professor  A.  P.  Carman  for  the  facilities  for  this  investigation  and  to 
Professor  Jakob  Kunz,  both  for  his  general  supervision  of  the  work  and 
for  many  valuable  suggestions. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS. 
May  6,  1912. 


{Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  I.,  No.  3,  March,  1913.] 


IONIZATION  OF  POTASSIUM  VAPOR  BY  ULTRA-VIOLET 

LIGHT. 

BY  S.  HERBERT  ANDERSON. 

THE  general  method  of  determining  the  ionization  of  potassium  vapor 
by  ultraviolet  light  consisted  in  measuring  the  current  produced  be- 
tween two  electrodes  which  were  contained  in  a  highly  exhausted  tube  con- 
taining potassium  vapor,  when  a  given  potential  difference  was  applied 
across  the  electrodes  and  a  beam  of  ultraviolet  light  passed  through  the 
vapor  between  the  electrodes. 

The  form  of  the  tube  used  is  shown  in  Fig.  I,  A.     The  tube  was  4  cm. 


Fig.  1. 

in  diameter  and  12  cm.  long.  It  was  closed  at  one  end  with  a  quartz 
plate  sealed  on  with  Bank  of  England  sealing  wax.  The  opposite  end 
of  the  tube  was  drawn  down  to  about  8  mm.  diameter  and  terminated  in 
a  bulb  b  in  which  the  potassium  k  was  lodged.  The  smaller  tube  was  bent 
around  in  a  semicircle  to  prevent  particles  shot  off  from  the  potassium 
from  penetrating  directly  the  space  between  the  electrodes.  The  potas- 
sium introduced  into  b  was  obtained  by  distillation  and  was  perfectly 
pure  and  clean.  The  tube  was  exhausted  by  a  Gaede  pump  and  then  by 
a  charcoal  bulb  and  liquid  air  to  the  best  possible  vacuum.  The  elec- 
trodes, e\  and  e2,  were  platinum  plates  6  X  2.5  cm.,  and  were  placed 
parallel  to  each  other  3  cm.  apart. 


2  34  5.  HERBERT  ANDERSON.  [!ER?ESD 

In  order  to  test  the  ionization  at  temperatures  higher  than  room 
temperature  the  tube  was  placed  in  an  electric  furnace  consisting  of  a 
copper  cylinder  on  which  were  wound  two  layers  of  wire  so  connected  that 
the  magnetic  field  within  was  negligible.  The  electric  furnace  containing 
the  tube  was  placed  in  a  sheet  iron  box,  tightly  closed  except  for  a  slit 
5  X  30  mm.  at  one  end,  which  could  be  opened  to  admit  ultraviolet  light. 
This  metal  box  was  connected  by  a  metal  tube  to  a  tight  metal  cylinder 
in  which  a  Dolezalek  electrometer  was  placed.  Electrode  e\  was  con- 
nected to  one  pair  of  quadrants  of  the  electrometer.  Electrode  6%  could 
be  grounded  or  connected  to  one  terminal  of  a  battery,  c  is  a  metal  collar 
about  the  tube  where  electrode  ei  is  sealed  in.  This  was  grounded  so  as 
to  prevent  conduction  over  the  outside  of  the  tube  from  effecting  the 
electrometer.  The  copper  cylinder  of  the  heating  coil  and  the  metal 
containers  of  the  heating  coil  and  electrometer  was  grounded,  E. 

When  the  tube  was  kept  in  darkness  at  room  temperature,  25°  C.,  no 
current  could  be  detected  with  the  electrometer  when  a  potential  differ- 
ence of  1,000  volts  was  maintained  between  the  electrodes.  When  a 
beam  of  ultraviolet  light  from  a  spark  between  zinc  electrodes  was  passed 
into  the  tube,  but  not  striking  the  electrodes,  and  the  same  potential 
difference,  1,000  volts,  was  maintained,  e%  being  connected  to  the  positive 
terminal  of  the  battery,  there  was  still  no  current.  (The  electrometer 
was  capable  of  indicating  a  current  of  io~13  amperes.)  If  however  the 
beam  of  light  was  incident  upon  the  electrode  connected  to  the  electrom- 
eter, there  was  a  deflection  and  the  direction  of  the  current  was  from 
ez  to  e\.  This  of  course  was  due  to  the  photo-electric  action  of  the  plati- 
num electrode.  Hence  there  was  no  indication  of  ionization  at  a  tem- 
perature of  25°. 

The  tube  was  then  heated  to  55°,  which  is  the  highest  temperature  to 
which  the  sealing  wax  may  be  heated  without  softening.  Two  hours  was 
required  for  this  heating,  in  order  to  get  a  constant  temperature.  At  this 
temperature  when  a  beam  of  ultraviolet  light  was  passed  between  the 
electrodes  there  was  a  comparatively  large  current,  the  values  of  which 
for  different  potential  differences  are  given  in  column  (a)  of  the  table. 
It  was  found  that  these  readings  could  not  be  duplicated  but  that  the 
current  increased  as  the  tube  was  maintained  at  this  temperature.  After 
four  hours  another  set  of  readings  was  taken  which  is  given  in  column 
(&).  The  tube  was  then  allowed  to  cool  down  to  room  temperature 
and  the  conductivity  tested  when  a  beam  of  ultraviolet  light  passed 
between  the  electrodes.  The  current  was  found  to  be  about  the  same  as 
that  found  by  the  last  set  of  readings  at  55°,  as  is  seen  by  comparing 
column  (c)  with  column  (b)  (Fig.  2). 


VOL.  I.- 

No.  3.  J 


I  ON  I Z  AT  I  ON  OF  POTASSIUM  VAPOR. 


235 


The  tube  was  in  perfect  condition  after  the  heating.  The  vacuum  was 
tested  by  a  spark  discharge  and  found  to  be  at  the  Rontgen  ray  stage. 
The  discharge  showed  some  of  the  characteristic  color  due  to  potassium 
vapor. 

In  the  table  the  current  is  given  in  terms  of  the  rate  of  deflection  of 
the  electrometer  needle  in  mm.  per  second.  A  deflection  of  20  mm.  per 
second  corresponds  to  a  current  of  io~12  amperes.  The  current  observed 
is  surprisingly  large  if  one  takes  into  consideration  the  fact  that  at  55°  the 
vapor  pressure  of  potassium  is  not  large.  The  minimum  current  observed 


TAfllg 

ffiSwS 


76.0 
1S6.0 
187.0 


Fig.  2. 


was  1.5  X  io~12  ampere,  that  is,  an  order  of  magnitude  quite  different 
from  the  currents  due  to  ionization  of  any  other  vapor  or  gas  by  ultra- 
violet light. 

The  increase  of  conductivity  as  the  tube  was  maintained  at  a  tem- 
perature of  55°  is  not  easy  to  explain;  nor  the  fact,  that  when  the  tube 
had  cooled  to  room  temperature  the  conductivity  was  about  the  same 
as  that  last  observed  at  55°,  while  in  the  first  place  there  was  no  current 
at  room  temperature.  However,  it  is  likely  that  this  is  closely  connected 
with  the  phenomenon  observed  by  Wood1  in  the  resonance  spectra  of 
mercury  vapor.  He  found  that  there  was  a  true  absorption  of  light  only 
when  the  pressure  of  the  gas  was  above  o.oi  mm.  When  a  small  amount 
of  air  was  introduced  so  that  the  pressure  was  raised  above  o.oi  mm.  the 
absorption  increased  with  the  pressure.  It  is  not  unreasonable  to  expect 
that  ionization  accompanies  the  transformation  of  light  energy  into  heat 
energy  that  occurs  in  true  absorption.  If  this  is  the  case  an  introduction 

1  Phil.  Mag.,  V.,  23,  p.  689,  1912. 


236  5.  HERBERT  ANDERSON.  [IS?*!! 

of  a  small  amount  of  air  or  other  gas  into  the  tube  of  this  experiment 
would  result  in  an  increase  of  conductivity.  In  this  experiment  it  is 
very  probable  that  gas  was  given  off  from  the  electrodes  and  walls  of 
the  tube  as  the  temperature  was  maintained  at  55°.  On  the  basis  of 
Wood's  discovery  this  then  would  account  for  the  increase  in  conductivity. 
No  deposit  of  potassium  was  observed  in  the  tube,  after  the  temperature 
had  been  raised  to  55°.  Moreover,  if  there  had  been  a  deposit  of  metal, 
it  would  have  occurred  during  the  distillation,  as  the  temperature  was 
then  above  200°,  and  yet  no  conductivity  or  ionization  was  noticeable 
until  the  tube  was  heated  to  55°.  It  is  the  intention  of  the  author  to 
extend  this  investigation  and  determine  this  point. 

SUMMARY. 

1.  Potassium  vapor  at  55°  is  readily  ionized  by  ultraviolet  light. 

2.  An  increase  of  ionization  is  produced  by  the  addition  of  a  small 
amount  of  foreign  gas. 

The  writer  is  indebted  to  the  Laboratory  of  Physics  of  the  University 
of  Illinois  for  the  facilities  and  to  Dr.  Kunz  for  suggestions  for  the  above 
work. 

UNIVERSITY  OF  WASHINGTON, 
November,  1912. 


(Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  I.,  No.  3.  March,  1913.] 


RECTIFYING   PROPERTIES  OF  A   PHOTO-ELECTRIC   CELL. 

BY  S.  HERBERT  ANDERSON. 

TT  has  long  been  known  that  a  photo-electric  cell  in  which  electrons 
•*•  are  freely  emitted  from  a  metal  under  the  action  of  light  has  distinct 
rectifying  properties.  In  some  investigations  by  Professor  Kunz  and 
Dr.  J.  G.  Kemp  it  was  found  that  in  a  photo-electric  cell  of  the  type  used 
by  the  author  in  the  present  investigation  may  be  used  as  a  detector  of 
electric  waves.  When  used  in  connection  with  a  Fleming  cymometer 
it  was  found  much  more  sensitive  than  the  neon  tube  furnished  with 
the  instrument.  Since  its  use  as  a  detector  depends  upon  its  rectifying 
property,  the  present  investigation  was  undertaken  to  determine  the 
adaptability  to  practical  use  in  wireless  telegraphy. 

DESCRIPTION  OF  METHOD  AND  APPARATUS. 

The  form  of  the  photo-electric  cell  used  is  shown  in  diagram  by  Fig. 
i,  A.  One  electrode  is  a  hemispherical  cap  of  pure  potassium  deposited 
in  the  lower  part  of  bulb  a,  which  is  4  cm.  in  diameter.  The  other  elec- 
trode is  a  platinum  point  b,  the  distance  of  which  from  c  can  be  adjusted 
by  the  action  of  a  magnet  on  the  iron  ring  d. 

The  method  of  preparing  the  potassium  was  the  same  described  in  a 
former  paper.1  The  potassium  collected  in  e  Was  poured  into  bulb  a 
and  deposited  on  the  lower  half  by  distillation.  It  was  desired  to  have 
the  cell  as  stable  as  possible  and  to  this  end  nitrogen  was  introduced  into 
the  tube  A.  For  removing  all  traces  of  oxygen  and  water  vapor  from 
the  nitrogen,  tube  B,  Fig.  i,  was  used.  Before  the  evacuation  of  the 
system  a  piece  of  potassium  was  introduced  into  the  tube  at  /  which  was 
then  sealed  off.  When  the  tube  was  evacuated  the  potassium  was  dis- 
tilled so  as  to  form  a  brilliant  metallic  surface  all  over  the  inside  of  B. 
With  stopcock  g  closed,  dry  nitrogen  was  let  into  B  through  h  at  atmo- 
spheric pressure.  The  potassium  near  h  turned  black  showing  some 
oxidation,  h  was  closed  and  the  tube  heated  until  again  there  was  a 
bright  metallic  surface.  This  insured  the  removal  of  all  oxygen  from  the 
gas.  Then  g  was  opened  and  nitrogen  let  into  A .  g  was  closed  and  the 
tube  A  pumped  out  until  the  discharge  from  a  small  induction  coil  passed 

1  PHYSICAL  REVIEW,  XXXV.,  p.  239,  1912. 


223  5-  HERBERT  ANDERSON. 

easily  between  the  electrodes  b  and  c.  Thus  in  a  rough  way  the  pressure 
of  minimum  sparking  potential  was  obtained.  When  a  potential  of  220 
volts  of  a  6o-cycle  alternating  current  was  applied  no  discharge  occurred, 
but  with  330  volts  a  current  of  about  o.i  ampere  passed.  A  was  then 
sealed  off  from  the  pump  at  k. 

The  method  used  in  examining  the  rectifying  properties  of  the  cell 
was  the  same  as  used  by  Pierce1  in  examining  the  crystal  and  electro- 
lytic detectors  and  is  shown  in  diagram  by  Fig.  2.  The  image  of  the 
luminous  spot  of  the  fluorescent  screen  of  a  Braun  tube  is  brought  to 
a  focus  on  a  drum  d  by  means  of  a  lens  /.  This  drum  is  connected  directly 
to  synchronous  motor  which  operates  on  a  no- volt,  6o-cycle  alternating 
current.  The  drum  is  covered  with  a  sensitive  photographic  film  and  is 
enclosed  in  a  light-tight  box.  The  source  of  the  current  sent  through 
the  photo-electric  cell  A  was  a  44o-volt,  6o-cycle  alternating  current 
supplied  by  the  same  dynamo  that  furnished  the  no-volt  circuit  that  the 
motor  was  operated  upon.  Thus  the  frequency  of  the  two  circuits  was 
the  same.  By  means  of  a  potentiometer  scheme  P  any  potential  dif- 
ference up  to  455  volts  (which  was  the  potential  across  the  so-called  440 
mains),  could  be  applied  to  the  electrodes  of  the  cell.  Connected  in 
series  with  A  were  a  pair  of  electromagnets,  c\  and  c%.  These  were  placed, 
one  above  and  the  other  below,  the  Braun  tube,  with  their  axes  in  a 
vertical  plane,  so  as  to  give  a  horizontal  deflection  to  the  narrow  cathode 
beam  which  passed  through  the  small  hole  in  the  metal  screen  s.  The 
total  resistance  of  the  electromagnets  was  381.8  ohms.  They  were  fitted 
with  cores  of  soft  Swedish  iron,  }/%  inch  in  diameter.  By  means  of  a 
double  throw  switch  5,  the  photo-electric  cell  could  be  replaced  by  a  non- 
inductive  resistance  R  which  was  adjusted  to  allow  the  same  current  to 
go  through  the  electromagnets  as  passed  when  the  cell  was  in  the  circuit. 
An  electrostatic  voltmeter  V  gave  the  fall  of  potential  across  the  electrodes 
of  the  cell. 

METHOD  OF  TAKING  OSCILLOGRAMS. 

In  Plate  I.,  (a),  (£>),  (c),  are  shown  three  of  the  oscillograms  taken, 
These  were  obtained  in  the  following  manner:  a  photographic  film  was 
placed  on  the  drum  d,  Fig.  2,  the  box  closed  and  a  cap  put  over  the  lens; 
the  motor  was  started  and  adjusted  to  run  in  synchronism;  the  switch 
5"  was  then  closed  so  that  the  alternating  current  potential  was  applied 
at  the  electrodes  of  the  cell  (the  current  which  passes  through  the  cell 
also  goes  through  the  electromagnets  and  the  alternating  magnetic  field 
produced  causes  an  alternating  deflection  of  the  cathode  beam,  so  that 
the  spot  of  light  on  the  fluorescent  screen  is  drawn  out  into  a  horizontal 

1  PHYSICAL  REVIEW,  XXVIII.,  p.  153,  1909. 


No"3L]  PROPERTIES  OF  A  PHOTO-ELECTRIC  CELL.  224 

line) ;  the  cap  was  then  removed  from  the  lens  and  the  image  of  the  spot 
of  light  moving  on  the  screen  was  thrown  upon  the  photographic  film. 
The  drum  was  rotated  in  synchronism  and  made  a  complete  rotation  for 
every  two  cycles  of  the  current.  So  the  spot  of  light  moved  over  the 
film  with  two  motions,  the  horizontal  motion  being  produced  by  the 
changing  magnetic  field  and  the  vertical  motion  produced  by  the  move- 
ment of  the  drum.  The  spot  of  light  started  in  at  the  same  point  at  the 
beginning  of  each  rotation.  The  part  of  the  oscillogram  obtained  by  this 
much  of  the  exposure  is  the  heavy  line  showing  loops  only  above  the 
horizontal  axis,  that  is,  a  current  in  one  direction  only.  The  switch  was 
then  thrown  so  that  R  was  in  the  circuit  instead  of  A .  The  part  of  the 
oscillogram  due  to  this  exposure  is  the  sine  curve.  The  switch  was  then 
opened  so  that  no  current  went  through  the  electromagnets  and  conse- 
quently there  was  no  horizontal  deflection.  This  exposure  gives  the  line 
of  the  axis  of  abscissas,  the  axis  of  zero  current.  The  time  of  exposure 
for  oscillogram  (b)  for  the  curve  of  the  rectified  current  was  2.5  minutes; 
for  the  non-rectified  current,  1.5  minutes;  for  the  line  of  the  horizontal 
axis,  40  seconds.  So  for  the  total  exposure  the  spot  of  light  moved  over 
the  film  8,400  times.  This  shows  that  the  motor  was  running  in  syn- 
chronism. 

For  oscillograms  (a)  and  (b)  the  ordinary  Eastman  kodak  films  were 
used.  For  oscillogram  (c)  an  Eastman  extra  rapid  film  was  used.  The 
times  of  exposures  for  the  three  curves  of  this  were  i'  50",  50"  and  30" 
respectively.  Probably  i',  30"  and  20"  would  be  plenty  of  time.  The 
lines  are  all  heavy  except  in  one  place,  where  the  film  may  have  been 
defective  or  was  not  evenly  developed. 

The  curve  obtained  when  the  current  passed  through  the  ohmic 
resistance  R  may  be  called  a  potential  phase  curve.  It  is  of  course  a 
current  curve,  but  since  the  potential  across  the  ohmic  resistance  is  in 
phase  with  the  current  through  that  resistance  it  gives  us  the  phase  of 
the  potential  about  the  photo-electric  cell,  and  enables  us  to  determine 
whether  or  not  there  is  any  lag  or  advance  of  the  current  through  the  cell. 
It  will  be  noticed  that  in  every  case  that  the  maximum  point  of  the 
rectified  curve  is  less  than  that  of  the  potential  phase  curve.  This  occurs 
in  spite  of  the  fact  that  in  every  case  great  care  was  taken  to  adjust  the 
resistance  R  before  the  exposure  for  an  oscillogram  so  that  the  maximum 
deflection  of  the  cathode  beam  was  the  same  for  the  current  passing 
through  R  as  it  was  for  the  current  passing  through  A.  But  as  the  cell 
is  used,  that  is,  as  a  current  passes,  the  resistance  of  the  cell  seems  to 
increase,  and  consequently  the  deflection  of  the  cathode  beam  decreases. 
This  is  shown  by  the  broad  line  of  the  curve  of  the  rectified  current  in 


225 


S.  HERBERT  ANDERSON. 


[SECOND 

[SERIES. 


oscillograms  (a)  and  (c)  especially.  During  the  exposure  for  each  of 
these  curves  the  current  decreased  about  0.5  milliampere,  or  10  per  cent. 
This  increase  of  the  resistance  seems  to  come  about  by  an  absorption  of 
the  gas  (nitrogen)  in  the  cell.  The  character  of  the  glow  discharge 
changed  in  such  a  way  as  to  show  a  decrease  in  pressure.  The  effect 
seemed  to  be  much  the  same  as  that  which  occurs  with  a  glow  discharge 
through  hydrogen  with  a  potassium  cathode  in  which  potassium  hydride 
is  formed.  But  with  this  difference,  that  in  the  cell  with  hydrogen  the 
potassium  hydride  formed  is  of  a  deep  violet  color,  becoming  almost 
black  if  the  discharge  is  continued  for  a  long  time.  But  with  the  cell 
containing  nitrogen  the  color  taken  on  by  the  potassium  under  the 
action  of  the  glow  discharge  is  at  first  bronze,  and  with  a  continuation 
of  the  discharge  the  color  becomes  a  bright  blue,  with  just  a  suggestion  of 
a  greenish  tinge.  On  heating  the  cell  until  the  potassium  is  melted  the 
color  disappears,  the  potassium  assumes  its  original  bright  metallic 
luster  and  the  pressure  is  increased.  It  seems  very  probable  that  a 
potassium  nitride  is  formed  by  the  glow  discharge.  Since  this  work  was 
done  a  reference1  has  been  found  giving  an  account  of  the  formation  of 
potassium  nitride  by  a  glow  discharge  between  a  potassium  cathode  and 
silver  anode  immersed  in  a  mixture  of  90  per  cent,  liquid  nitrogen  and  10 
per  cent,  liquid  argon;  and  also  the  account  states  that  the  nitride  is 
formed  when  the  liquid  nitrogen  is  replaced  by  gaseous  nitrogen. 


Fig.  2. 


In  taking  all  these  oscillograms  the  amount  of  light  falling  on  the  photo- 
electric cell  was  rather  faint.  There  was  an  eight-candle-power  red- 
globed,  incandescent  lamp  about  three  meters  distant  from  the  cell; 
and  the  cell  was  exposed  to  the  faint  light  from  the  Braun  tube.  It  was 
noticed  just  after  oscillogram  (b)  was  taken  that  light  falling  on  the  cell 
had  a  marked  effect  on  the  action.  If  the  cell  was  in  total  darkness  and 

1  Ber.  der  deutschen  Chemischen  Gesellschaft,  Vol.  43.  p.  1465,  1910. 


PHYSICAL  REVIEW,  VOL.  I.,  SECOND  SERIES. 
March,  1913 


PLATE  I. 
To  face  page  226 


S.  HERBERT  ANDERSON 


VOL.  I. 
No.  3.  . 


PROPERTIES  OF  A  PHOTO-ELECTRIC  CELL. 


226 


the  potential  applied  there  was  no  discharge  in  the  tube  and  no  measurable 
current  passed.  But  if  a  i6-candle-power  lamp  at  a  distance  of  a  meter 
was  turned  on  the  discharge  occurred  and  continued  after  the  light  was 
turned  out.  But  by  the  deflection  of  the  cathode  beam  it  was  noticed 
that  the  current  was  about  6  per  cent,  less  when  the  cell  was  in  darkness 
than  when  it  was  illuminated  by  the  i6-candle-power  lamp  at  the  distance 
of  I  meter.  If  however  the  lamp  was  brought  up  to  a  distance  of  40  cm. 
from  the  cell,  the  discharge  stopped,  but  started  again  when  the  light 
was  moved  away.  This  shows  that  the  light  intensity  has  a  very  marked 
effect,  as  well  as  the  gas  pressure  and  the  electrode  distance.  It  is  very 


Fig.  3. 

probable  that  the  discharge  continued  after  the  light  was  turned  out  be- 
cause of  the  action  of  the  light  produced  by  the  discharge  in  the  cell 
upon  the  potassium. 

TABLE  I. 


Oscillogram. 

/  in  Amperes. 

FR.M.S.  Value  in  Volts. 

Electrode   Distance  (in 
Centimeters). 

(a) 

0.004 

390 

4.1 

W 

0.005 

455 

4.7 

(<0 

0.003 

370 

4.7 

DISCUSSION   OF   OSCILLOGRAMS. 

In  Table  I.  are  given  the  maximum  values  of  the  rectified  current, 
/;  the  R.M.S.  voltage  across  the  electrodes,  F;  and  the  electrode 
distance  for  each  oscillogram.  The  divisions  of  the  scales  along  the 
oscillograms  represent  milliamperes.  Time  is  represented  in  a  horizontal 
direction  from  left  to  right. 


227  5-  HERBERT  ANDERSON. 

The  characteristic  features  of  the  oscillograms  are:  (i)  That  the  recti- 
fication is  complete,  that  is,  the  current  is  transmitted  in  only  one  direc- 
tion ;  (2)  the  form  of  the  current  curve  in  the  rectified  cycle ;  (a)  there  is 
a  lag  in  rising  from  the  axis  of  zero  current ;  (b)  the  curve  up  to  the  maxi- 
mum point  is  nearly  a  straight  line ;  (c)  the  curve  of  decreasing  current  is 
of  an  exponential  form;  (d)  the  lag  at  the  end  of  the  half  cycle  is  very 
much  less  than  at  the  beginning,  just  how  much  is  difficult  to  determine 
because  of  the  exponential  form  of  the  curve. 

The  degree  of  rectification  in  this  type  of  cell  is  shown  by  another 
experiment.  A  cell  of  the  same  form  and  dimensions,  but  employing 
potassium  hydride  as  the  active  electrode  and  hydrogen  for  the  gas  was 
tried  with  a  direct-current  potential.  400  volts  had  to  be  applied  at  the 
electrodes  before  a  current  would  pass  which  could  be  measured  by  a 
milliammeter.  With  this  potential  there  was  a  glow  discharge  in  the 
tube.  When  electrode  c,  Fig.  I,  was  connected  to  the  negative  terminal 
of  the  battery  and  b  to  the  positive,  the  current  was  100  milliamperes. 
When  the  terminals  were  reversed,  the  current  was  0.05  milliampere. 
The  current  then  passing  in  one  direction  was  2,000  times  as  great  as  the 
current  in  the  opposite  direction.  Such  a  ratio  is  much  larger  than  could 
be  shown  by  the  oscillograms. 

In  general  the  cause  of  rectification  in  this  kind  of  a  cell  is  readily 
explained.  When  the  potassium  electrode  is  connected  to  the  negative 
terminal  of  the  source  of  potential  and  the  platinum  point  to  the  positive, 
electrons  are  given  off  readily  by  a  photo-electric  action.  With  such  a 
potential  as  was  used  a  very  faint  light  is  sufficient  to  start  the  discharge 
of  electrons.  When  the  field  is  in  the  opposite  direction  no  electrons 
can  be  given  off  when  the  potential  difference  is  greater  than  that  arising 
from  the  photo-electric  action.  However  the  current  due  to  the  electrons 
alone  is  of  a  very  much  lower  value  than  that  obtained  here.  The 
author  found  (1.  c.)  the  electron  current  from  a  potassium  electrode  of  about 
one  fourth  the  area  used  in  this  experiment  was  6  X  io~10  amperes  for  the 
same  electrical  field.  However  the  light  intensity  was  much  greater  than 
in  the  present  investigation.  But  assuming  that  the  number  of  electrons 
leaving  unit  area  of  the  potassium  electrode  is  the  same  in  the  two  cases, 
and  hence,  that  the  current  due  to  the  electrons  in  the  present  investiga- 
tion is  about  24  X  io~10  amperes,  even  then  this  is  insignificant  compared 
with  the  total  current.  So  the  carriers  of  the  current  must  be  chiefly 
ions  which  are  produced  by  collisions  of  the  electrons  with  the  mole- 
cules of  the  gas.  As  the  potential  across  the  electrodes  rises  from  a  zero 
value  to  a  maximum,  c  being  negative  and  b  positive,  the  current  that 
can  be  detected  is  negligible  until  the  potential  difference  reaches  such  a 


NoL'3L]  PROPERTIES  OF  A  PHOTO-ELECTRIC  CELL.  22% 

value  that  the  electrons  have  sufficient  velocity  to  produce  ions  by 
collision.  This  is  indicated  by  the  point  where  the  current  curve  rises 
sharply  from  the  axis  of  zero  current  in  the  oscillograms.  From  this  point 
on  as  the  potential  increases  to  a  maximum  there  is  a  two-fold  increase  in 
the  conductivity  due  (i)  to  the  increase  in  the  rate  of  production  of  ions 
and  (2)  the  increase  in  the  velocity  of  the  ions.  As  the  potential  de- 
creases the  conductivity  decreases  in  a  two-fold  manner.  Thus  we  see 
that  the  current  will  not  be  a  sine  function  because  the  resistance  is  not  a 
constant.  It  is  not  possible  to  determine  analytically  the  form  of  the 
current  curve  until  the  function  which  shows  how  the  resistance  varies  is 
known.  When  the  potential  falls  below  the  critical  value  necessary  for 
the  production  of  ions  there  are  some  ions  still  left  in  the  space  between 
the  elecrtodes,  and  the  current  from  this  point  on  until  the  potential 
becomes  zero  is  due  to  the  movement  of  these  ions  to  the  electrodes. 
When  the  impressed  E.M.F.  reverses  and  c  becomes  positive  and  b 
negative,  the  electron  current  is  zero,  and  hence  the  source  of  ionization  is 
zero  and  there  is  no  current. 

By  the  application  of  the  equations  for  alternating  currents  we  can 
determine  whether  the  characteristics  of  the  current  curve  are  due  to 
any  of  the  factors  of  the  circuit  besides  the  photo-electric  cell.  The 
potential  phase  curve  was  obtained  when  the  circuit  contained  only 
resistance  and  the  self-inductance  of  the  magnetizing  coils.  The  dif- 
ferential equation  of  such  a  circuit  with  an  impressed,  simple,  harmonic 
E.M.F.  is 

Rii  +  L~  =  £  sin  co/,  (i) 

at 

the  solution  of  which  is 


When  the  current  has  reached  a  steady  state  the  exponential  term  becomes 
negligible.  Of  the  constants  of  the  circuit  R  and  co  are  known,  but  L  is 
not.  This  may  be  determined  by  taking  the  expression  for  the  maximum 
value  of  ii 


The  R.M.S.  value  of  the  voltage  across  the  electromagnets  was  1.5  volts 
at  the  time  oscillogram  (b)  was  taken.  The  maximum  value  of  the  cur- 
rent, taken  from  the  oscillogram,  was  0.005  ampere.  The  resistance  of 
the  coils  was  381.8  ohms.  The  maximum  voltage  is  given  by 

'         =  2.12  VOltS. 


0.707 


229  5-  HERBERT  ANDERSON. 

We  may  then  obtain  Leo  from  (3) ,  where  E  is  the  maximum  voltage  across 
the  coils  and  R  is  the  resistance. 

2.12 

=  l/ (381.8)'+!^' 
Leo  =  184.4. 

In  order  to  obtain  the  potential  phase  curve  a  resistance  of  82,800  ohms 
had  to  be  introduced  into  the  circuit  in  place  of  the  cell.  The  angle  of 
lag  of  the  current  in  this  circuit  behind  the  impressed  E.M.F.  is  given  by 

Leo 
arc  tan  —  ,  (4) 

where  R  is  the  total  resistance  of  the  circuit  and  is  82,800  +  382  ohms. 

Leo  184.4 

arc  tan     -  =  arc  tan —  =  0.128  . 

R  83,182 

That  is,  the  lag  of  the  so-called  potential  phase  curve  behind  the  impressed 
E.M.F.  is  0.128°.  From  measurements  on  oscilligram  (b)  it  was  deter- 
mined that  the  current  in  the  rectified  cycle  lagged  0.109  part  of  a  period 
or  39.24°  behind  the  potential  phase  cycle.  Hence  the  total  lag  of  the 
rectified  cycle  behind  the  impressed  E.M.F.  is 

39.24  +  0.128  =  39.368°. 

We  can  find  the  voltage  across  the  electrodes  at  which  the  current  rises 
above  the  axis  of  zero  current  by  the  expression 

eQ  =  E  sin  39.368°, 

where  E  is  the  maximum  value  of  the  voltage.  The  R.M.S.  value  of  the 
voltage  was  455  volts. 

643.5 voits.    ••- ;;;_  _/:    ..; 

eQ  =  643.5  sin  39.368°  =  408  volts. 
The  equation  for  the  current  through  the  cell  is  given  by 

diz 
E  sin  eo£  —  er  =  Rci%  +  L  -,—,  (5) 

where  er  is  the  potential  drop  across  the  photo-electric  cell.  Since  er 
is  a  function  of  the  current  i%  the  form  of  this  function  must  be  known 
in  order  to  integrate  the  above  expression.  This  function  is  represented 
by  the  function  potential  curve.  Unfortunately  the  author  was  unable 
to  take  such  a  curve  with  this  cell.  In  Fig.  3  is  shown  a  current  potential 
curve  taken  by  Dr.  J.  G.  Kemp  for  a  cell  filled  with  hydrogen  at  3  mm. 


No"3!']  PROPERTIES  OF  A  PHOTO-ELECTRIC  CELL. 

pressure  and  using  an  electrode  distance  of  3.0  cm.  Undoubtedly  the 
curve  for  the  cell  the  author  used  was  of  the  same  type.  The  analytical 
expression  for  this  curve  has  not  been  determined,  but  for  certain  regions 
of  the  curve  the  relation  between  the  current  and  the  potential  can  be 
expressed  approximately  by  a  linear  equation.  In  the  curve,  Fig.  3,  the 
maximum  value  of  the  current  was  about  io~8  amperes,  which  is  a  much 
lower  order  of  value  than  the  currents  obtained  in  this  investigation. 
Hence  it  is  very  probable  that  the  expression  for  er  for  the  range  o.ooi 
to  0.005  ampere  is 

er  =  e0  +  ri,  (6) 

where  eQ  is  the  intercept  of  the  axis  of  potentials  and  r  is  the  resistance 
of  the  cell.  Of  course  the  resistance  varies  greatly  and  any  value  of  r 
that  might  be  determined  would  only  hold  for  a  small  range  of  the  current. 
Substituting  the  value  of  er  given  by  (6)  in  (5)  we  have 

di 
E  sin  co/  -  e0  =  (r  +  Rc)iz  +  L  —  .  (7) 


Integrating  this  equation  we  get 

I 

m  I  co/  — 
" 


E  I  Leo   \          -r-+^t          e0 

sm  I  co/  —  arc  tan  —  ;—  =-  1  +  ce      L 
" 


. 
r+R, 

We  may  take  eQ  to  be  the  voltage  that  must  be  placed  across  the  electrodes 
before  a  measurable  current  will  pass,  that  is,  408  volts.  In  order  to 
determine  a  value  of  r,  take  the  maximum  value  of  i2  from  the  rectified 
cycle.  Then  in  equation  (6) 

er  =  E  =  643.5  volts, 

iz  =  /  =  0.005  ampere. 
Therefore 

643.5  =  408  -f  r  X  0.005, 

r  =  46,900  ohms. 

This  then  gives  the  resistance  of  the  cell  at  the  instant  of  maximum 
current. 

The  exponential  term  in  (8)  becomes  negligible  within  a  very  short  time 
after  the  circuit  is  closed  and  hence  should  not  occur  in  an  equation 
dealing  with  current  at  the  time  the  oscillograms  were  taken,  when  a 
steady  state  has  been  reached.  It  is  apparent  then  that  the  current 
curve  given  by  equation  (8),  when  the  exponential  term  is  dropped  out, 
will  be  a  sine  curve  with  a  lag  of  arc  tan  Lco/(r  +  Rc)  and  with  the  axis 
of  abscissae  raised  by  an  amount  eo/(r  +  Rc).  As  previously  pointed 
out  the  current  curve  cannot  be  a  sine  curve,  hence  we  cannot  use  this 


231  S.  HERBERT  ANDERSON. 

equation  for  determining  anything  about  the  current  except  at  the  instant 
of  maximum  value.  We  can  determine  then  what  the  lag  is  at  this 
instant. 

Leo  184.4 

arc  tan  -  — ^r  =  arc  tan  — —  =  0.224  . 
r  +  Rc  47,282 

This  is  the  largest  lag  possible  arising  from  the  self-inductance  of  the 
circuit  as  r  has  a  minimum  value  for  the  maximum  value  of  the  current. 
In  as  much  as  this  angle  is  smaller  than  can  be  detected  on  the  oscillo- 
grams,  we  may  conclude  that  the  lag  in  the  current  is  due  to  the  prop- 
erties of  the  cell  as  previously  noted,  and  not  to  other  factors  of  the  circuit. 

Every  electric  wave  detector  of  the  rectifying  type  is  of  use  as  a 
detector  either  (i)  because  of  its  rectifying  properties,  or  (2)  because 
its  current  potential  curve  is  not  linear.1  Inasmuch  as  the  photo-electric 
cell  possesses  both  of  these  properties  it  may  be  used  in  two  ways,  as 
Dunwoody2  has  shown  crystal  detectors  may  be  used.  In  case  the 
rectifying  property  is  made  use  of  the  efficiency  depends  upon  the  degree 
of  rectification.  As  in  the  photo-electric  cell  the  power  of  rectification 
is  of  a  very  high  order,  it  should  prove  as  efficient  as  any  detector  used. 
It  could  be  used  either  with  a  telephone  or  a  sensitive  galvanometer. 
It  has  the  advantage  of  giving  a  glow-discharge  when  a  current  is  passing, 
so  the  receipt  of  a  call  by  wireless  could  be  noted  by  the  operator  without 
the  use  of  the  telephone. 

The  author  is  now  attempting  to  find  the  most  sensitive  condition  of 
the  cell  for  detecting  electric  waves,  and  intends  to  test  thoroughly  its 
efficiency. 

CONCLUSION. 

1.  The  rectifying  power  of  a  photo-electric  cell,  using  potassium  for 
the  active  electrode,  has  been  found  to  be  of  the  ratio  2,000  to  I. 

2.  The  general  form  of  the  rectified  cycle  is  the  same  for  the  different 
pressures,  electrode  distances  and  potentials  used. 

3.  The  amount  of  the  current  for  a  given  potential  depends  on  the 
pressure  of  the  gas,  the  electrode  distance,  and  the  intensity  of  light 
falling  on  the  cell;  but  does  not  increase  continuously  with  increasing 
intensity. 

4.  Nitrogen  at  a  pressure  of  about  5  mm.  combines  with  potassium  or 
is  absorbed  by  it  when  a  glow  discharge  passes. 

5.  The  high  power  of  rectification  and  the  high  resistance  of  the  photo- 
electric indicate  that  it  may  be  very  efficient  as  a  detector  of  electric 
waves. 

1  Fleming,  Principles  of  Wireless  Telegraphy  and  Telephony,  p.  474. 

2  U.  S.  Patent  Specifications,  No.  837,  616,  1906. 


NoL'3L]  PROPERTIES  OF  A  PHOTO-ELECTRIC  CELL  2 $2 

The  author  takes  pleasure  in  acknowledging  his  indebtedness  to  Dr. 
J.  G.  Kemp  for  the  type  of  cell  used  and  for  the  curve  of  Fig.  3,  to  Pro- 
fessor Kunz  for  many  valuable  suggestions  and  assistance  in  preparing 
the  cells  used,  and  to  Professor  Carman  and  the  physics  department  of 
the  University  of  Illinois,  where  the  investigation  was  carried  on,  for  the 
facilities  and  means  for  the  work. 

PHYSICS  DEPARTMENT, 

UNIVERSITY  OF  WASHINGTON, 
October,  1912. 


REPRINTED  FROM  ENGINEERING  RECORD 
VOLUME  67,  PAGE  265,  MARCH  8, 1913 


Air  Currents  and  Their  Relation  to  the  Acoustical 
Properties  of   Auditoriums 

With  Application  of  the  Conclusions  to  Ventilating  Systems 

By  F.  R.    Watson,  Ph.D.,    Assistant  Professor  of   Physics,  University  of  Illinois 


When  looking  up  the  references  for  the 
subject  of  architectural  acoustics  an  ac- 
count was  found  of  "some  experiments  made 
for  the  purpose  of  determining  the  effects 
of  the  currents  of  air  within  an  auditorium 
upon  its  acoustical  qualities."  (W.  W.  Jacques. 
"Effect  of  the  Motion  of  the  Air  within  an 
Auditorium  upon  Its  Acoustical  Qualities." 
"Philosophical  Magazine"  (5),  vol.  7,  page  in, 
1879.)  Jacques  found  by  experiment  that  the 
ventilating  system  of  the  Baltimore  Academy 
of  Music  was  so  arranged  that  it  had  a  very 
pronounced  action  on  the  acoustics.  He  writes : 
"According  to  a  survey,  made  with  the  thistle 
balls  and  the  anemometer,  of  the  space  con- 
tained within  the  walls  of  this  theatre,  the 
movement  of  the  air  is  as  follows :  The  whole 
supply  of  fresh  air  is  admitted  at  the  back  of 
the  stage,  is  there  warmed,  then  crosses  the 
stage  horizontally,  passes  through  the  prosce- 
nium, and  then,  somewhat  diagonally  toward 
the  roof,  across  the  auditorium  in  one  grand 
volume  and  with  gentle  motion  so  as  to  almost 
entirely  prevent  the  formation  of  minor  air 
currents.  It  is  exhausted  partially  by  an  out- 
let in  the  roof  and  partly  by  numerous  regis- 
ters in  the  ceilings  of  the  galleries.  From  this 


Fig.  i 

central  outlet  and  from  the  large  flues  of  the 
registers,  the  air  passes  into  the  ventilating 
tower  over  the  great  chandelier,  which  sup- 
plies, in  its  heat,  a  part  of  the  motive  power  of 
the  circulation.  .  .  .  The  acoustics  are,  if 
we  may  judge  from  the  testimony  of  a  large 


number  of  singers  and  speakers,  as  well  as 
from  our  own  observation,  among  the  best. 
The  weakest  voice  is  audible  to  every  seat  in 
the  house;  sounds  such  as  a  sigh,  a  kiss,  or 
even  the  simulated  breathing  of  the  somnambu- 
list, may  be  heard  in  the  most  distant  parts; 
and  all  effects  in  music  are  exactly  rendered. 
All  singers  and  speakers  agree  in  describing 
the  facility  with  which  the  voice  is  used  on 
this  stage." 

Jacques  carried  out  experiments  to  show 
that  the  acoustics  were  affected  by  the  ar- 
rangement of  the  current  of  air.  "For  this 
purpose,"  he  writes,  "persons  have  been  re- 
peatedly stationed  at  different  parts  of  the. 
house  during  a  performance,  without  being  in- 
formed of  the  nature  of  the  experiments  to 
be  carried  out.  They  have  been  simply  asked 
to  note,  at  intervals  during  the  evening,  the 
comparative  ease  with  which  they  could  hear 
the  performers.  At  various  intervals  during 
the  evening  the  valves  which  control  the  venti- 
lation were  reversed,  so  as  to  entirely  inter- 
fere with  the  unbroken  condition  of  the  air 
and  give  rise  to  currents  of  circulation.  Al- 
most invariably  the  testimony  of  the  hearers 
would  be  that,  at  times  corresponding  to  the 
interruption  of  the  ventilation,  the  'sound  was 
dead,  was  confused  and  indistinct';  and  it 
would  be  observed  that  people  all  over  the 
house  would  make  an  effort  to  listen." 

This  action  of  an  air  current  seemed  so  re- 
markable that  further  confirmation  was  sought 
from  other  sources.  The  result  of  the  search 
showed  that  both  theory  and  experiment  sup- 
port the  results  set  forth  by  Jacques — that  an 
air  current  may  affect  the  progress  of  sound 
waves,  although  the  effect  is  small  for  ordinary 
conditions.  It  is  further  indicated  that  the  ar- 
rangement of  the  ventilating  system  is  one  of 
the  factors  that  may  affect  the  acoustics  of  a 
room.  Thus  it  can  be  shown  theoretically  that 
a  stream  of  heated  air  can  reflect  and  refract 


sound  waves,  the  magnitudes  of  these  effects 
being  proportional  to  the  temperature  of  the 
stream  and  to  other  less  important  factors. 
This  deduction  is  supported  by  laboratory  ex- 
periments and  by  conditions  that  have  been 
noted  in  auditoriums.  By  means  of  the  theory 
the  experimental  phenomena  can  be  explained 
and  the  general  conditions  written  down  for 
the  arrangement  of  the  ventilation  current  that 
will  be  most  beneficial  for  the  acoustics. 

THEORY 

Lord  Rayleigh  has  developed  the  general  re- 
lations whereby  the  reflection  and  refraction  of 
sound  at  the  boundarv  of  two  media  may  be 


Fig.  2 

calculated.  ("Theory  of  Sound,"  vol  2,  section 
270.  See  also  equations  at  end  of  paper.) 
He  shows  that  for  perpendicular  incidence  at 
a  surface  between  air  and  hydrogen  about  one- 
third  of  the  energy  is  reflected.  For  the  case 
of  two  layers  of  air,  one  at  o  deg.  C.  and  the 
other  at  10  deg.  C.,  only  about  83/100,000  of 
the  energy  is  reflected — much  less  than  the  case 
for  air-hydrogen  because  the  difference  in 
density  is  correspondingly  less.  When  the 
temperature  difference  between  the  layers  of 
gas  increases  the  amount  of  energy  reflected 
also  increases.  Thus,  for  a  difference  of  27.3 
deg.  the  energy  reflected  is  55/10,000;  for  237 
deg.,  1/30  is  reflected.  Another  instance  of 
small  density  difference  is  the  case  for  two 
layers  of  air  at  10  deg.  C.,  one  of  which  is 
saturated  with  water  vapor,  while  the  other 
is  dry.  Only  1/744,000  part  of  the  energy  is  re- 
flected. Rayleigh  concludes  that  "reflections 
from  warm  or  moist  air  must  generally  be 
small,  though  the  effect  may  accumulate  by 
repetition." 

For  oblique  incidence,  however,  more  en- 
ergy is  reflected  than  for  perpendicular  inci- 
dence. When  the  angle  of  incidence  is  suffi- 
ciently oblique,  theory  shows  that  total  reflec- 
tion follows.  Thus,  for  the  case  of  two  layers 
of  air,  one  10  deg.  warmer  than  the  other,  the 
angle  for  total  reflection  is  79  deg.  7  min. ; 
that  is,  the  angle  between  the  direction  of 
propagation  of  the  sound  waves  and  the  sur- 


face of  separation  of  the  warm  and  cold  air 
is  10  deg.  53  min.  This  means  that  waves  must 
strike  very  obliquely  for  total  reflection.  For 
the  layers  of  dry-moist  air  the  angle  is  more 
oblique,  namely,  86  deg.  8  min.  for  total  reflec- 
tion. For  less  oblique  angles  the  reflection  is 
less,  being  practically  zero  for  angles  less  than 
that  for  total  reflection. 

In  addition  to  the  reflection  that  takes  place 
at  the  boundary  between  two  media  there  oc- 
curs also  a  refraction,  or  bending  in  direction, 
of  the  sound  waves  that  enter  the  second 
medium.  For  instance,  a  beam  of  sound  waves 
striking  obliquely  at  the  boundary  between  cold 
and  warm  air  would  be  bent  toward  the  bound- 
ary as  it  enters  the  warm  air. 

A  number  of  experiments  are  cited  that  con- 
firm the  theory.  Tyndall  showed  that  a  high- 
pitched  sound  was  easily  reflected  by  the  flame 
of  a  bat's-wing  gas  burner.  (Tyndall,  "On 
Sound/'  1898  edition,  page  319.)  For  this  case 
the  temperature  difference  between  the  air  and 
the  flame  is  great,  so  that  the  density  difference 
is  also  great,  and  a  large  reflection  would  be 
expected.  The  author  has  repeated  Tyndall's 
experiment  for  conditions  somewhat  different. 
Sound  waves  of  about  2  cm  wave  length  were 
generated  by  means  of  a  Galton  whistle  and 
directed  against  the  vertical  sheet  of  hot  gas 
rising  above  a  straight  row  of  gas  flames.  The 
waves  were  reflected  by  the  gas  column  and 
detected  with  a  sensitive  flame  for  both  per- 
pendicular and  oblique  incidence. 

Sabine  describes  an  interesting  case  that 
shows  the  effect  of  heated  currents  of  air  in  a 
room.  (Engineering  Record,  vol.  61,  page 
780,  1910.)  In  a  court  room  in  Illinois  a  stove 
was  situated  in  the  center  of  the  room.  In 
winter  when  the  stove  was  heated  great  diffi- 
culty in  hearing  the  judge's  remarks  was  ex- 
perienced by  those  whose  position  was  such 
that  the  stove  stood  between  them  and  the 
judge.  In  the  summertime,  when  the  stove  was 
not  in  use,  the  trouble  disappeared.  The  ex- 
planation of  the  effect  follows  from  the  pre- 
vious theory.  The  ascending  column  of  air 
from  the  stove  was  so  hot  that  it  reflected  and 
refracted  the  sound  to  such  an  extent  that 
little  was  left  to  pass  on  directly  to  the  audi- 
tors in  the  rear  of  the  room. 

Tyndall  describes  another  experiment  in 
which  he  placed  a  series  of  gas  currents  be- 
tween a  source  of  sound  and  a  receiver.  ("On 
Sound,"  page  312.)  The  sound  was  entirely 
cut  off.  Suppose  A  (see  Fig.  i)  to  be  the 
source  of  sound  and  B  the  receiver.  A  was  a 
bell  of  high  pitch  and  B  a  sensitive  flame.  At 


the  places  marked  -f-  imagine  currents  of 
illuminating  gas  to  rise.  At  places  marked  — 
imagine  descending  currents  of  cold  carbon 
dioxide.  As  the  sound  goes  out  from  A,  a 
portion  is  reflected  back  from  each  boundary 
between  the  gas  columns,  so  that  finally  there 
is  little  or  no  sound  left  that  gets  through  to  B 
to  affect  the  flame.  In  this  case  a  large  effect 
is  to  be  expected,  since  the  densities  of  the 
gases  are  very  different. 

APPLICATION     TO     STREAM     OF    AIR     IN     AN 
AUDITORIUM 

The  previous  theory  may  now  be  used  to  ex- 
plain the  effect  of  a  current  of  air  such  as  the 
one  investigated  by  Jacques  in  the  Baltimore 
Academy  of  Music.  Assume  that  the  current 
of  air  is  27.3  deg.  (for  convenience  of  calcula- 
tion) warmer  than  the  air'  in  the  room,  and 
that  it  moves  in  one  large  stream  from  the 
stage  to  the  walls  at  the  rear  of  the  auditorium. 
Calculations  show  (see  theory  at  end  of  paper) 
that  the  sound  waves  that  strike  the  boundary 
between  warm  and  cold  air  are  practically  all 
transmitted  except  for  those  waves  that  strike 
very  obliquely.  These  latter  waves  become 
totally  reflected.  The  transmitted  waves  are 
bent  in  direction  as  they  pass  into  a  medium  of 
different  density.  The  state  of  affairs  is  indi- 
cated in  Fig.  2.  Inspection  shows  that  the  ef- 
fect of  the  air  current  is  to  bend  the  sound  in 
the  direction  of  the  stream,  but  this  effect  is 
seen  to  be  small. 

We  now  pass  to  the  case  of  the  haphazard 
currents  and  attempt  to  explain  why  Jacques 
found  the  sound  confused  and  indistinct.  For 
this  case  there  are  a  number  of  currents  of  air 
of  different  densities,  with  many  boundaries 
set  up  between  hot  and  cold  gases.  Each 
boundary  has  its  effect  in  reflecting  and  re- 
fracting the  sound  waves  so  that  the  resultant 
effect  is  complex.  Furthermore,  if  it  be  con- 
sidered that  these  currents  are  not  steady,  but 
that  each  one  fluctuates  more  or  less,  it  is  seen 
that  the  effect  at  any  one  point,  say  the  ear  of 
the  observer,  is  "confused  and  indistinct."  The 
result  is  much  the  same  as  the  analogous  case 
in  optics  where,  on  a  summer's  day,  objects 
at  a  distance  appear  quivering  and  distorted 
because  of  the  intervening  ascending  currents 
of  warm  air.  So  in  the  auditorium  the  sound 
which  is  clear  and  distinct  after  passing 
through  a  homogeneous  medium  may  well  be- 
come distorted  when  it  goes  through  a  num- 
ber of  unsteady  streams  of  unequally  heated 
air.  * 


Jacques'  experiments  bear  out  this  conclu- 
sion about  the  indistinctness  produced  by  tiie 
varying  currents.  He  writes  that  10  to  15  min- 
utes were  required  for  the  air  currents  to  be- 
come steady  after  the  ventilation  had  been  re- 
versed. During  this  time  of  unsteady  currents 
the  observers  reported  the  hearing  confused 
and  indistinct. 

This  last  conclusion  is  confirmed  by  a  num- 
ber of  experiments.  Jacques  set  up  an  ap- 
paratus so  that  the  sound  of  an  organ  pipe  was 
diffracted  to  the  rear  side  of  a  large  board 
placed  vertically  in  such  a  position  as  to  set  up 
interference  of  the  sound.  When  the  air  in 
the  room  was  at  rest,  these  positions  of  inter- 
ference were  easily  detected  with  a  resonator. 
The  case  was  analogous  to  the  optical  phe- 
nomenon where  light  is  diffracted  around  a 
similar  obstacle  so  as  to  produce  interference. 
When  the  windows  were  opened  to  allow  the 
cold  winter  air  to  pour  in,  and  also  when  the 
registers  were  opened  to  admit  currents  of  air 
at  100  deg.  C,  the  phenomena  of  interference 
instantly  disappeared.  The  experiment  was  re- 
pealed many  times,  always  with  the  same  re- 
sult. 

Experiments  by  the  author  confirm  this  re- 
sult described  by  Jacques:  In  a  laboratory 
about  25  ft.  square  a  whistle  was  blown,  while 
a  receiver — a  Rayleigh  suspended  disc — was 
placed  across  the  room  and  responded  to  the 
sound.  Small  air  currents  caused  a  difference 
in  the  deflections,  while  a  draft  from  a  window 
through  the  door  made  large  fluctuations  in 
the  readings.  Steady  deflections  were  almost 
impossible  to  obtain  with  air  currents  in  the 
room. 

FURTHER  EXPERIMENTS  BY  JACQUES 

In  this  same  connection  Jacques  performed 
another  experiment.  He  set  up  conditions 
analogous  to  Tyndall's  experiment  (see  Fig. 
i ),  so  as  to  approximate  the  state  of  affairs  in 
an  auditorium.  Thus,  at  places  marked  -f-  ne 
placed  "substances  heated  to  such  tempera- 
tures as  to  give  rise  to  currents  of  air  cor- 
responding in  density  to  those  found  in  an 
auditorium.  At  A  was  placed  a  source  of 
sound,  being  in  some  cases  an  organ  pipe,  in 
others  a  man  who  spoke  in  a  clear  and  distinct 
voice,  and  in  others  various  musical  instru- 
ments on  which  simple  combinations  of  notes 
were  played.  At  B  was  placed  the  ear,  .  .  . 
the  best  instrument  imaginable  for  determin- 
ing the  qualities  of  the  sounds."  The  experi- 
ments showed  that  the  clear  notes  of  the  or- 
gan pipe  lost  not  only  decidedly  in  intensity 


but  also  in  distinctness.  The  effect  on  the 
man's  voice  was  to  decrease  the  intensity,  and 
also  to  make  it  slightly  confused  and  indistinct, 
as  if  each  syllable  was  repeated  several  times 
in  very  close  succession.  With  a  flute  the  ef- 
fect was  the  same  as  for  a  man's  voice.  The 
effect  on  a  violin  seemed  to  be  considerably 
less.  With  a  drum  no  effect  whatever  was 
observed.  Jacques  concludes:  "Currents  of 
air  of  varying  density,  then,  cause,  first,  a  de- 
crease in  intensity  of  sound,  and,  second,  an 
indistinctness  or  confusion  of  sound." 

Another  instance  of  the  same  nature  is  men- 
tioned by  Sabine  (loc.  cit.).  In  the  House  of 
Commons  in  1835  "  a  current  of  hot  air,  rising 
in  a  broad  sheet  along  the  center  of  the  house, 
reflected  the  sound  passing  from  side  to  side 
and  rendered  the  intonation  indistinct.  One  of 
the  members  .  .  .  stated  that  he  had  often 
noticed  that  he  could  not  hear  a  member  op- 
posite him  distinctly  at  particular  times  unless 
he  shifted  his  position  along  the  bench,  and 
on  examining  the  place  referred  to  it  was 
found  that  he  had  moved  to  a  position  where 
the  hot  air  current  no  longer  passed  between 
him  and  the  member  speaking." 

The  conclusion  to  be  drawn  from  Jacques' 
experiments  is  that  haphazard  currents  in  an 
auditorium  are  detrimental  to  the  acoustics.  It 
is  not  to  be  concluded  that  the  other  arrange- 
ment of  the  air  current  in  one  large  stream 
will  be  of  great  benefit  unless  a  very  great  dif- 
ference of  temperature  is  set  up  between  the 
heated  current  and  the  surrounding  air. 
Jacques  simply  showed  that  such  a  stream  had 
only  a  little  effect  in  distorting  the  sound. 
Probably  the  acoustics  were  good  without  any 
ventilation,  and  it  is  to  be  regretted  that 
Jacques  records  no  experiments  performed 
with  the  ventilation  entirely  cut  off.  Such  an 
experiment  would  have  shown  whether  the 
good  acoustical  properties  were  due  to  the 
arrangement  of  the  ventilation  or  to  the  other 
features  of  the  room. 

AUTHOR'S  EXPERIMENTS 

The  author  has  performed  some  experi- 
ments suggested  by  these  conclusions  to  deter- 
mine whether  or  not  heated  air  currents  in 
a  room  cut  down  the  duration  of  sound.  Thus, 
if  air  currents  reflect  much  sound  they  ought 
to  act  as  reflectors,  or  extra  partitions,  and 
multiply  the  number  of  the  reflections  of  the 
sound  per  second.  Since  a  fraction  of  the 
energy  of  the  sound  waves  is  absorbed  at  each 
reflection,  the  presence  of  the  air  currents 
would  decrease  the  duration  of  the  sound.  The 


experiment  involved  Sabine's  well-known 
method  ("American  Architect,"  1900),  where 
the  absorbing  power  of  substances  for  sound 
may  be  determined  by  measuring  the  time  of 
duration  of  the  "residual  sound" — i.  e.,  the 
sound  that  persists  after  the  source  of  sound 
is  stopped.  In  a  room  about  20  ft.  square, 
cleared  of  all  furniture,  an  organ  pipe  was 
sounded  for  several  seconds  and  then  stopped. 
The  time  taken  for  the  sound  to  die  out  was 
noted  by  an  observer,  the  record  being  made 
electrically  on  a  chronograph  drum.  The  ob- 
servation was  repeated  when  two  long  rows 
of  gas  burners,  placed  on  the  floor,  were 
lighted.  In  this  case  there  were  two  sheets  of 
hot  gas  to  interfere  with  the  progress  of  the 
sound.  Further  data  were  obtained  with  the 
gas  flames  extinguished;  also,  a  fourth  meas- 
urement with  two  windows  open.  The  results 
follow,  the  figuring  representing  duration  of 
the  residual  sound  after  the  source  of  sound 
was  stopped : 

(a)  For  room  with  bare  walls 3-155  sec. 

(b)  With  burners  lit 2.960  sec. 

(c)  With  two  windows  open 2.512  sec. 

It  is  seen  that  the  effect  is  small,  but  in  the 

right  direction  to  confirm  the  theory.  The  ab- 
sorbing power  of  the  gas  currents  is  very 
small,  since  the  two  open  windows  with  very 
much  smaller  area  have  a  much  greater  effect. 
Hence,  air  currents  in  an  auditorium  cannot 
be  expected  to  have  any  pronounced  effect  as 
absorbers  of  sound. 

MINOR  FACTORS  AFFECTING  SOUND  WAVES 

In  order  to  complete  the  discussion  of  the 
effect  of  a  current  of  air  on  the  acoustics  in 
an  auditorium  there  should  be  considered  sev- 
eral other  factors  of  minor  importance  that 
may  affect  the  progress  of  the  sound  waves — 
namely,  the  presence  of  moisture  in  the  air, 
the  motion  of  the  stream,  and  the  effect  of  the 
carbon  dioxide  breathed  out  by  the  auditors. 
The  presence  of  moisture  would  have  but  lit- 
tle effect  on  the  sound  waves,  since  it  has  al- 
ready been  shown  for  the  extreme  case  where 
the  air  in  the  stream  is  saturated  with  mois- 
ture and  the  surrounding  air  completely  dry 
that  the  effect  is  small.  Under  usual  condi- 
tions the  air  in  the  stream  would  not  be  satu- 
rated, neither  would  the  air  surrounding  the 
auditors  be  completely  dry;  therefore,  the  ef- 
fect would  be  still  smaller  and  may  be  disre- 
garded. The  motion  of  the  air  can  be  shown 
"to  have  a  negligible  effect  provided  the  velocity 
of  the  stream  is  not  more  than  60  cm.  (about 
2  ft.)  per  second.  (See  theory  at  end  of 


paper.)  This  statement  seems  to  contradict 
the  well-known  action  of  the  wind  whereby 
sounds  may  be  heard  a  long  distance  from  the 
source.  For  this  case  the  action  follows  be- 
cause the  wind  may  act  on  the  sound  for  a 
long  distance.  Also,  a  high  velocity  of  the 
wind  may  intensify  the  effect.  Neither  the 
condition  of  long  distance  action  nor  of  high 
velocity  is  found  in  the  usual  air  currents  in  an 
auditorium;  hence  the  motion  has  a  negligible 
effect. 

It  should  be  pointed  out  that  the  theory  de- 
veloped by  Lord  Rayleigh  assumes  certain  re- 
strictions with  which  the  conditions  in  an 
auditorium  are  at  variance  in  some  respects. 
Thus,  the  transition  layer  between  the  two 
media  should  be  small  compared  with  the 
wave  length  of  the  incident  sound.  If  it  be 
assumed  that  the  wave  lengths  of  ordinary 
sounds  for  women's  voices  range  from  2  to  6 
ft.  and  for  men  from  4  to  18  ft.  (Winkelmann, 
"Hanclbuch  der  Physik,"  vol.  2,  page  686),  and 
further  that  the  transition  layer  between  warm 
and  cold  air  has  a  thickness  of  i  ft.,  it  is  seen 
that  the  theoretical  condition  is  not  fulfilled 
for  the  sounds  of  short-wave  length.  That  is, 
reflection  would  take  place  fairly  completely 
for  the  deep  bass  tones,  but  those  of  high  pitch 
would  be  readily  transmitted.  The  sounds  ut- 
tered by  a  man  would  suffer  more  reflection 
than  those  by  a  woman;  the  notes  of  a  bass 
viol  would  be  more  affected  than  the  high  notes 
of  a  violin.  The  theory  also  assumes  the  sound 
waves  to  be  plane,  whereas  in  an  auditorium 
they  are  spherical  as  they  come  from  a  speaker. 
At  some  distance  from  the  source  the  waves 
would  become  flatter,  hence  would  accord  more 
closely  with  the  theory. 


CONCLUSIONS 


The  previous  discussion  has  shown  both 
from  theory  and  experiment  that  sound  waves 
impinging  on  the  boundary  between  two  gases 
suffer  reflection  and  refraction.  The  magni- 
tude of  the  effects  depends  chiefly  on  the  dif- 
ference in  density  in  the  two  gases.  The  differ- 
ence of  density,  in  turn,  depends  on  the  differ- 
ence in  temperature  of  the  gases,  or  difference 
in  moisture  content,  or  because  the  two  gases 
are  different  in  nature  Many  of  the  common 
effects  of  gas  currents  on  sound  may  be  ex- 
plained by  these  considerations.  It  is  shown 
that  haphazard  currents  of  air  in  an  audi- 
torium make  the  hearing  confused  and  indis- 
tinct. 

The  principles  evolved  suggest  certain  ar- 
rangements in  an  auditorium  that  will  help  the 


acoustics.  Hot  stoves,  radiators  and  hot  air 
registers  should  be  placed  near  the  walls  of  the 
room  so  that  no  very  hot  currents  of  air  be- 
come interposed  between  speaker  and  auditors 
(see  Sabine,  loc.  cit).  In  theaters  it  would 
be  an  advantage  to  have  footlights  made  up  of 
incandescent  lights  instead  of  gas  lamps,  since 
the  latter  set  up  a  sheet  of  hot  gas  between 
the  players  and  the  audience,  with  detriment 
to  distinct  hearing.  The  ventilation  in  an 
auditorium  has  practically  no  effect  unless  the 
currents  are  haphazard.  For  this  case  the 
sound  becomes  confused  and  indistinct.  The 
best  arrangement  of  the  ventilation  is  to  have 
it  pass  in  steady  streams  with  as  few  boundar- 
ies as  possible,  and  with  gentle  motion  so  that 
no  strong  drafts  are  set  up.  It  is  not  to  be 
concluded  that  poor  acoustics  in  an  auditorium 
may  be  greatly  improved  by  a  ventilating  sys- 
tem. What  is  to  be  concluded  is  that  the 
acoustics  may  be  made  worse  when  the  cur- 
rents of  air  are  unsteady  with  many  boun- 
daries between  hot  and  cold  layers. 

It  is  not  without  interest  to  apply  the  con- 
clusions brought  forth  to  other  systems  of  ven- 
tilation than  the  one  described  by  Jacques. 
Conference  with  Prof.  J.  M.  White,  supervis- 
ing architect  of  the  University  of  Illinois,  has 
brought  forth  the  following  discussion: 

In  order  to  ventilate  an  audience  room  the 
air  must  either  be  brought  in  through  numer- 
ous openings  in  the  floor  at  a  low  velocity  and 
at  a  temperature  of  about  70  deg.  Fahr.,  or  it 
must  be  brought  in  at  a  higher  temperature 
and  velocity  through  wall  registers.  With  the 
latter  method  it  is  difficult  to  bring  the  air 
down  to  the  breathing  zone.  The  case  de- 
scribed by  Jacques  is  of  this  type.  It  seems 
likely  that  the  heated  stream  of  fresh  air 
passes  over  the  heads  of  most  of  the  audience 
and  is  breathed  only  by  those  in  the  upper  gal- 
leries, where  the  air  is  drawn  out.  Such  a  cur- 
rent of  warm  air  might  be  valuable  as  a  heat- 
ing medium,  because  there  is  usually  a  large 
loss  of  heat  through  the  roof  of  an  audience 
room.  Suppose  the  stream  of  air  is  not  taken 
out  at  the  roof  but,  after  being  cooled  by  con- 
tact with  the  upper  surface  and  wall  of  the 
room,  falls  to  the  floor  and  is  taken  out  by 
outlets  so  distributed  as  to  give  the  greatest 
probability  of  its  traveling  across  the  breathing 
zone.  For  this  case  it  would  be  of  value  both 
for  heating  and  ventilating,  but  would  give 
haphazard  currents  which  would  be  detri- 
mental to  good  acoustics. 

Consider  now  the  other  method  of  ventila- 
tion. The  warm  air  comes  through  the  floor 


and,  rising  about  the  audience,  is  further 
heated  and  goes  vertically  to  the  outlets  in  the 
ceiling.  Some  of  the  warm  air  becomes  cooled 
by  contact  with  the  cold  walls  and  falls  back 
to  the  floor,  thus  setting  up  haphazard  cur- 
rents; the  main  effect  is,  however,  to  give  a 
large  stream  of  air  of  nearly  uniform  tempera- 
ture and  velocity.  Its  effect  on  the  sound 
would  be  small.  In  case  the  auditorium  were 
in  the  center  of  the  building  and  surrounded 
by  warm  rooms  the  effect  on  the  sound  would 
be  still  less,  since  there  would  be  no  descend- 
ing cold  currents  of  air  at  the  side  walls. 

Considering  all  the  circumstances,  this  last 
arrangement  seems  to  be  the  best  one  for 
acoustics.  As  already  pointed  out,  it  would  be 
more  advantageous  to  have  the  uniform  stream 
start  from  the  stage  and  go  with  the  sound; 
but  this  plan  has  greater  disadvantages  for  the 
ventilation.  Professor  Sabine,  from  a  some- 
what different  line  of  reasoning,  has  come  to 
the  same  conclusion — namely,  that  the  vertical 
stream  of  air  is  best  for  the  acoustics  (loc. 
cit.). 

Lord  Rayleigh  has  developed  the  general  re- 
lations whereby  reflection  and  refraction  of 
sound  at  the  boundary  of  two  media  may  be 
calculated.  ("Theory  of  Sound,"  vol.  2,  sec- 
tion 270.)  Imagine  two  different  gases,  each 
homogeneous,  lying  one  above  the  other  so  that 
the  dividing  plane  is  horizontal.  (See  Fig.  3.) 
A  train  of  plane  waves  striking  this  boundary 
more  or  less  obliquely  will  be  partly  reflected 
and  partly  transmitted,  the  transmitted  por- 
tion being  refracted.  The  equation  applying 
to  the  case  in  hand  follows  from  the  general 
relations  and  reads : 


9 


Where  9"  and  9'  are  the  amplitudes  respective- 
ly of  the  reflected  and  incident  waves,  V  the 
velocity  of  sound  in  the  medium  of  density  p 


UfperMedium 
Density*p, 
Velocity^, 


that  contains  the  incident  waves,  and  V±  and 
p!  the  corresponding  values  for  the  other  me- 
dium, 6  is  the  angle  between  the  normal  to  the 
boundary  plane  and  the  direction  of  propaga- 
tion of  the  incident  waves. 

REFLECTION  OF  SOUND 

From  the  equation  may  be  calculated  the 
ratio  of  the  amplitude  of  the  reflected  wave  to 
that  of  the  incident  wave;  or,  better  still,  the 
ratio  of  the  energies,  since  the  energy  is  pro- 
portional to  the  square  of  the  amplitude. 

For  perpendicular  incidence  at  a  surface  be- 
tween air  and  hydrogen  Lord  Rayleigh  has 
calculated  that  about  one-third  of  the  energy 
is  reflected.  Inspection  of  equation  (i)  shows 
that  for  perpendicular  incidence  0  =  o,  and 
tan  6  =  0,  so  that  the  relation  reduces  to 


This  may  be   further  simplified  by  using  the 
relation  for  the  velocity  of  sound  in  gases 

(3) 


where  p  is  the  pressure  of  the  gas,  ?  the 
density  and  8  the  ratio  of  the  specific  heats. 
The  ratio  of  the  velocities  for  air  and  hydro- 
gen is 


since  p  has  the  same  value  for  both  gases  at 
the  boundary  and  8  is  the  same  (1.41)  for  air 
and  hydrogen.  The  densities  of  air  and  hydro- 
gen are  respectively  0.001276  and  0.00008837. 
Equation  (i)  may  now  be  written 


9"/Y  =  (i  —  Vp/pJ  -f-  (i  + 

=  -  (2.8/4.8)      (4) 
The  energy  relation  follows: 

(9'02=(2.8/4.8)2(9T  =  0.34(9')'; 
that  is,  about  one-third  of  the  incident  energy 
is  reflected. 

For  the  case  of  two  layers  of  air,  one  at 
o  deg.  C.  and  the  other  at  10  deg.,  only  about 
80/100,000  of  the  energy  is  reflected.  Before 
calculating  the  temperature  effect  it  is  better 
to  simplify  equation  (2).  This  may  be  done 
by  taking  VJV  =  VP/Pi  and  using  the  relation 
for  the  change  in  density  with  the  tempera- 
ture :  p/pt  =  i  -f~  0.00366  1,  where  p  is  the 
density  at  o  deg.  and  ^  the  density  at  t  deg.  C. 
above  zero.  Equation  (2)  becomes: 


9"       i  —  V  J  —  0.00366  t 
9'        i  -f-  V I  +  0.00366  t 


(5) 


For  t  =  10  deg.,  9"/V  =  — 0.0089,  and  the 
ratio  of  the  energies,  (9")Y(<p')2  =  0.000079, 
which  shows  that  only  a  very  small  part  of  the 
energy  is  reflected.  For  a  greater  difference 
of  temperature  more  energy  is  reflected.  Thus, 
for  t  =  273  deg.,  9"/9'  =  0.171  and  cp"2/?" 
=  0.0289,  so  that  about  1/30  of  the  incident 
energy  is  reflected.  Another  case  of  the  same 
kind  is  that  of  two  layers  of  air  at  10  deg., 
one  of  which  is  saturated  with  water  vapor, 
while  the  other  is  dry.  The  ratio  of  the  densi- 
ties is: 

pt  (moist  air)  _  220 
p  (dry  air)       221 

Substituting  these  values  in  equation  (4), 
9///9/  =  —  0.00224,  and  9"2/9'2  =  0.00000502. 

OBLIQUE  INCIDENCE 

When  the  incidence  departs  from  the  per- 
pendicular— that  is,  when  0  increases  from 
o  deg. — the  theory  shows  that  the  amount  of 
reflected  energy  gets  less  until  a  value  of  0  is 
reached  for  which  9"/9'  —  °-  This  indicates 
total  transmission,  with  none  of  the  energy  re- 
flected, since  the  amplitude  of  the  reflected 
wave  is  zero.  The  condition  for  this  result 
is  that  the  numerator  of  the  fraction  equal 
zero — i.  e., 


or 


Inspection  of  the  last  relation  shows  that  tan  0 
is  real  only  when  the  two  parentheses  are 
either  both  positive  or  both  negative.  This 
condition  is  obtained  when  the  value  for  V/V^ 
lies  intermediate  between  p'/p  and  i.  Other- 
wise the  value  for  tan  0  is  imaginary  and  total 
transmission  will  not  take  place. 

As  6  increases  beyond  this  value  the  in- 
cidence becomes  more  oblique  and  more  energy 
is  reflected  until  another  critical  value  of  6  is 
reached  for  which  total  reflection  takes  place. 
For  this  value  9"/V  —  i,  or  the  amplitude  of 
the  reflected  wave,  equals  that  of  the  incident 
wave  and  all  the  energy  is  reflected.  The  con- 
dition for  this  value  is  that 

tan20(F12/F2-i)  -  i.  (7) 

An  application  of  all  the  foregoing  relations 
to  the  case  of  two  layers  of  air,  one  at  o  deg. 
and  the  other  at  27.3  deg.,  gives  the  following 
results : 


mtic  cncrgy  rcflected- 


rcflectionde— 

43°  50'  0.0000000     zero  reflection;  total  transmission. 

50°  0.00021      ] 

60°  0.000439    ^reflection   increases. 

70°  0.1005       J 

72°  30'  1.0000  total  reflection. 

72°  30'  up  to  90°  total    reflection. 

An  inspection  of  these  values  shows  that  the 
reflection  is  practically  zero  until  the  angle  of 
incidence  gets  very  oblique.  Therefore,  for 
small  temperature  difference  in  the  layers  of 
gas  the  sound  would  be  almost  all  transmitted 
except  for  the  rays  that  strike  at  very  oblique 
angles  of  incidence.  For  a  greater  difference 
in  the  temperature  the  effect  is  more  marked. 
Thus,  when  one  air  layer  is  at  o  deg.  and  the 
other  at  273  deg.  C.  about  1/30  of  the  energy 
is  reflected  for  perpendicular  incidence.  Total 
transmission  takes  place  when  0  =  35  deg.  14 
min.,  and  total  reflection  begins  when  0  reaches 
the  value  of  45  deg.  A  still  greater  effect  is 
found  in  the  case  of  air  hydrogen  already 
mentioned  for  perpendicular  incidence.  For 
this  case  total  transmission  comes  for  0  = 

14  deg.  45  min.  and  total  reflection  for  0  = 

15  deg.    15   min.     This   transition   from  total 
transmission  to  total  reflection  is  very  sudden. 
A  consideration  of  these  results  leads  to  the 
conclusion  that   no  great  reflection  of  sound 
is  to  be  expected  between  two  layers  of  gas 
unless  the  temperature  difference  is  great  or 
else  the  gases  differ  greatly  in  density.     As 
Rayleigh  points  out,  however,  the  effect  may 
accumulate  by  repetition. 

EFFECT  OF  MOTION  OF  AIR 
Bernoulli's  equation  gives  the  relation 

/>/p  -f-  M2/2  +  U  =  />0/po  +  M02/2  +  Uo 


where  p  is  the  pressure  in  a  stream  of  fluid, 
p  the  density,  and  u  the  velocity,  and  U  the 
internal  energy.  For  gases  such  as  air,  oxygen, 
etc.,  U  =  cvT  with  sufficient  exactness,  where 
cv  is  the  specific  heat  for  constant  volume 
and  T  is  the  absolute  temperature.  By  using 
also  the  relation  for  gases  pv  =  RT,  or 
/>/p  =  RT,  Bernoulli's  equation  becomes 


t>  U      .     Cvp 

— 1 —   =• 

P  2  flp 


cvp 


or 


since  it  may  be  shown  that  R  =  cp  —  cv, 
where  cp  is  the  specific  heat  for  constant  pres- 
sure. Substituting  8  =  cp/cv  in  the  relation 
F2  =  8/>/p,  where  V  is  the  velocity  of  sound, 
there  is  obtained 


8-1 


i  — i 


Applying  this  equation  to  the  moving  stream 
of  air,  the  left-hand  side  of  the  equation  may 
refer  to  a  point  in  the  stream  where  the 
velocity  is  u  and  the  right-hand  side  to  any 
other  point.  For  this  other  point  choose  a 
place  where  the  velocity  is  practically  zero— 
i.  e.,  where  V0  is  the  velocity  of  sound  in  air 
at  rest.  The  equation  becomes 


_ 
2  ~: 


8  — 


from  which  the  ratio  V/V0  may  be  calculated 
if  u  is  given.  This  ratio,  V/V0,  may  be 
thought  of  as  the  ratio  of  the  velocity  of 
sound  in  the  stream  to  the  velocity  of  sound 
outside  the  stream,  since  the  air  outside  the 
stream  is  at  rest.  Assuming  u  =  60  cm  per 
second  and  V0  =  34,500  cm  per  second,  V  is 
calculated  to  be  34,499  cm  per  second;  that  is, 
practically  the  same  as  V0.  Therefore,  prac- 
tically no  reflection  would  occur  at  the  boun- 
dary of  a  moving  stream  of  air,  since  V/V0  is 
practically  equal  to  unity,  and  substitution  in 
equation  ( i )  would  give  9"/V  =  ° — i-  e->  no 
reflection. 


CONDITIONS  OF  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS 
WITH  ALKALI  METALS  AND  HYDROGEN. 

BY  J.  G.  KEMP. 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  I.,  No.  4,  April,  1913.] 


CONDITIONS  OF  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS 
WITH   ALKALI   METALS  AND   HYDROGEN. 

BY  J.  G.  KEMP. 

THE  object  of  this  investigation  is  a  systematic  quantitative  study 
of  the  conditions  of  sensibility  of  photo-electric  cells  of  alkali  metals 
with  hydrogen  and  a  determination  of  the  work  required  to  draw  an 
electron  out  of  an  atom. 

The  photo-electric  phenomena  are  very  important  in  connection  with 
the  theory  of  radiation,  and  for  photometric  purposes.  Planck's  theory 
of  radiation  requires  that  the  potential  due  to  incident  light  should  in- 
crease proportional  to  the  frequency  of  the  light.  Moreover,  if  the 
theory  of  the  units  of  energy  strikes  reality,  we  should  expect  that  the 
photo-electric  current  for  very  weak  intensities  of  light  becomes  inter- 
mittent, as  the  electrons  are  given  out  only  from  time  to  time,  so  that 
the  phenomenon  should  resemble  the  radioactive  scintillator.  If  the 
intensity  of  the  incident  light  falls  below  a  critical  value,  an  electron  can 
only  escape  from  the  metal,  if  its  kinetic  energy  is  at  least  equal  to  the 
unit  of  energy  received  from  the  beam  of  light.  Photometric  measure- 
ments have  already  been  carried  out  by  Elster  and  Geitel,  by  Richtmeier,1 
by  E.  L.  Nichols  and  E.  Merritt.2  As  the  sensitiveness  of  the  photo- 
electric cells  is  very  great,  comparable  indeed  with  the  sensitiveness  of 
the  selenium  cell,  we  hope  to  use  these  photo-electric  cells  for  the  measure- 
ment of  the  light  from  the  fixed  stars. 

The  sensitiveness  of  the  photo-electric  cells  has  been  increased  con- 
siderably by  the  formation  of  an  alkalihydride  and  by  replacing  hydrogen 
by  helium.  This  has  been  done  by  Elster  and  Geitel.3 

The  work  necessary  to  produce  an  ion  can  be  determined  by  two  inde- 
pendent methods.  One  method  is  based  on  the  ionization  by  a  particles, 
the  other  on  the  potential  difference  which  in  a  discharge  tube  is  necessary 
to  produce  ionization  by  collision.  The  results  of  the  two  methods  do  not 
satisfactorily  agree  with  each  other.  A  larger  number  of  determinations 
of  this  quantity  is  necessary  before  we  can  explain  the  difference  of  the 
results. 

1  PHYSICAL  REVIEW,  29,  p.  71,  1909. 

*  PHYSICAL  REVIEW,  34,  p.  475,  1912. 

1  Physik.  Zeitschrift,  n,  April,  1910,  and  August,  1911. 


'Iron  ffiny 


$£4!']  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS.  2J$ 

DESCRIPTION  OF  APPARATUS. 

It  was  required  to  find  the  sensitiveness  of  the  photo-electric  cells  as 
function  of  the  gas  pressure,  the  electrode  distance,  the  area  of  metal 
illuminated,  the  voltage  applied  to  the  electrodes  and  the  intensity  of 
illumination.  Fig.  I  shows  the  glass  tube  used  in  making  the  cell.  A 
spherical  bulb,  2.5  cm.  in  diameter,  has  two  tubes  i.o  cm.  in  diameter, 
sealed  horizontally  and  diametrically  oppo- 
site each  other.  A  vertical  tube,  1.8  cm. 
in  diameter,  about  15  cm.  long  is  sealed  in 
the  top  of  the  bulb. 

At  the  top  of  this  vertical  tube  a  plati- 
num wire  is  sealed  and  fused  to  an  alumi- 
num rod  0.4  cm.  in  diameter  and  10  cm.  in 
length.  To  the  lower  end  of  the  aluminum 
rod  is  attached  a  brass  spiral  spring  to 

which  is  connected  the  platinum  wire  an-     f      ^ 

ode.     The  anode,  a,  being  sealed  through     Q  \  ^       ,  -A 

the  lower  end  of  the  glass  tube  which  tele-  ^3-^ 

scopes  the  aluminum  rod.     At  the  upper  end  Fig  j 

of  this  glass  tube  is  attached  an  iron  ring 

which  fits  neatly  inside  the  larger  tube.  By  means  of  an  electromagnet, 
using  a  current  of  2  amperes,  the  inner  tube  carrying  the  anode,  a,  can 
be  held  in  any  desired  position  relative  to  the  cathode,  c,  at  the  bottom 
of  the  bulb. 

At  the  bottom  of  the  bulb  and  diametrically  opposite  the  anode,  a, 
is  sealed  the  cathode,  c,  the  upper  point  of  which  does  not  extend  beyond 
the  surface  of  the  inside  of  the  bulb.  In  some  of  the  cells  the  inside  of 
the  lower  surface  of  the  bulb  was  silvered,  the  metal  distilled  into  it 
and  deposited  upon  the  mirror  surface.  In  this  way  a  good  contact  was 
insured  between  the  platinum  and  the  metal.  In  some  of  the  tubes 
the  metal  was  not  distilled  into  the  bulb  but  poured  into  it  while  in  the 
molten  state  and  allowed  to  solidify  over  the  platinum  electrode.  The 
metal  in  all  cases  was  used  as  the  cathode  of  the  cell.  In  order  to  form 
the  sensitive  hydride  the  alkali  metal,  that  is,  the  cathode,  was  connected 
to  the  negative  terminal  of  a  battery  of  300  or  400  volts  while  a  resistance 
of  3,000  ohms  and  a  galvanometer  was  placed  in  series  with  the  positive 
terminal  of  battery  and  the  anode  of  the  cell.  The  pressure  of  the 
hydrogen  gas  in  the  cell  was  then  reduced  until  the  current  flowing 
between  anode  and  cathode  caused  a  faint  glow  to  fill  the  whole  tube. 
The  metal  surface,  which  was  very  bright  before  the  illumination  ap- 
peared in  the  tube,  afterward  became  colored,  being  brownish  for  sodium, 


276 


J.  G.  KEMP. 


[SECOND 

[SERIES. 


bluish  violet  for  potassium,  and  light  greenish  for  rubidium  and  caesium. 
These  colors  are  due  to  the  formation  of  a  compound  of  the  hydrogen 
and  the  metal,  which  is  called  a  hydride.  When  the  hydrogen  is  replaced 
by  argon  or  helium,  the  cell  maintains  its  high  sensitiveness  constant  for 
a  long  time.  And  even  if  the  metal  remains  in  contact  with  hydrogen, 
the  sensitiveness  did  not  seem  to  change  during  the  few  days  in  which 
the  readings  were  taken. 

The  distance  between  the  electrodes  could  be  changed  by  means  of 
an  electromagnet,  arranged  inside  the  light-tight  box,  and  a  cathetom- 
eter  was  used  for  the  accurate  determination  of  the  electrode  distance. 

Fig.  2  shows  the  entire  arrangement  of  the  apparatus  for  the  investi- 
gation. The  photo-electric  cell  is  enclosed  in  a  light-tight  box.  Wires 
connected  to  the  anode  and  cathode,  and  to  the  electromagnet,  M,  pass 


forth 


Fig.  2. 

through  insulators  in  the  walls  of  the  box.  The  cell  is  sealed  to  the 
system  containing  a  Macleod  gauge  for  measuring  pressures  up  to  0.24 
cm.,  a  closed  manometer  for  measuring  the  higher  pressures,  a  regulator 
for  obtaining  small  variations  in  pressure,  a  tube  containing  palladium 
metal  strips  for  supplying  pure  hydrogen  gas,  and  an  air  pump  The 
palladium  metal  was  charged  with  hydrogen  gas  by  the  electrolytic 
method.  With  an  electrolyte  of  one  part  of  H2SO4  and  three  parts  of 
H2O,  the  anode  being  platinum,  and  the  palladium  metal  the  cathode, 
hydrogen  gas  was  absorbed  by  the  cathode  when  2.5  volts  was  connected 
across  the  electrodes.  After  charging  the  palladium,  the  tube  containing 
it  was  sealed  to  the  system.  When  the  tube  is  heated  with  a  small 
bunsen  flame,  the  metal  gives  off  pure  hydrogen  gas.  The  whole  glass 
system,  when  the  pump  was  cut  off,  could  be  filled  to  a  pressure  of  about 
25  cm.  when  the  palladium  was  heated. 


"4']  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS. 

The  galvanometer  used  is  a  Leeds  and  Northrup  type  HS,  the  sensi- 
bility being  3.78  X  io~10  amp.  per  mm.  Deflection  for  2  meters  scale 
distance.  The  anode  of  the  cell  was  connected  to  the  earth  through  the 
galvanometer  and  a  megohm  resistance.  The  cathode  of  the  cell  was 
connected  to  a  variable  point  in  a  water  rheostat  which  is  in  series  with 
about  640  volts  from  a  storage  battery.  The  voltage  applied  to  cathode 
could  be  varied  by  means  of  the  water  rheostat  and  it  was  measured  by 
a  Kelvin  electrostatic  voltmeter  reading  0-600  volts. 

The  variation  of  the  area  of  the  metal  illuminated  was  obtained  by 
varying  the  opening  of  the  iris  diaphragm  A,  which  is  placed  at  the 
lower  end  of  a  brass  tube.  This  tube  was  blackened  on  the  inside  to 
prevent  reflection  of  light. 

By  moving  the  lamp  on  the  guide  the  intensity  of  illumination  on 
the  metal  in  the  photo-electric  cell  could  be  varied,  and  this  variation 
calculated  directly  by  means  of  the  inverse  square  law. 

METHOD. 

Since  the  most  sensitive  conditions  for  the  photo-electric  effect  are 
being  sought,  it  is  necessary  to  study  the  effect  due  to  varying  all  the 
possible  conditions  in  order  to  find  the  most  effective  set  of  conditions. 
The  variables  in  this  work  are  the  following:  P  the  pressure  of  the  gas, 
D  the  distance  between  the  electrodes,  V  the  potential  difference  applied 
to  electrodes,  A  the  area  of  metal  illuminated,  L  the  intensity  of  illumina- 
tion, t  the  temperature  of  the  cell,  and  d  the  galvanometer  deflection 
which  is  proportional  to  the  current. 

Two  sets  of  readings  are  possible  for  each  cell,  namely,  before  forming 
and  after  forming  the  hydride  surface.  In  this  paper  this  process  will 
be  called  forming. 

Four  cells  were  studied:  one  with  caesium  and  three  with  potassium 
metal.  The  readings  were  taken  in  the  order  as  follows:  With  /,  Z,,  A, 
P  and  D  constant  the  values  of  the  deflections,  d,  of  the  galvanometer  were 
read  for  increasing  values  of  V.  Thus  values  of  current  and  voltage 
were  obtained  for  an  ionization  curve.  This  was  repeated  for  three  and 
in  some  cases  four  distances  of  D. 

From  the  above  data  four  ionization  curves  are  obtained  which  show 
the  effect  of  varying  the  distance  between  the  electrodes  for  constant 
values  of  /,  L,  A  and  P.  If  the  above  three  or  four  ionization  curves 
be  called  a  set,  then  it  is  possible  to  get  as  many  sets  as  there  are  values 
of  P,  the  gas  pressure.  From  three  to  five  different  values  of  P  were 
selected  for  each  cell  and  in  this  way  the  effect  due  to  change  of  pressure 
was  studied. 


J.G.  KEMP.  [f£°g; 

lonizatioh  curves  were  also  obtained  in  which  A,  L,  P  and  D  are 
constant  for  three  or  four  different  temperatures.  After  the  forming 
process  similar  sets  of  ionization  curves  were  taken  except  those  for 
temperature  changes.  In  addition  to  the  ionization  curves  taken  after 
forming  the  cell  No.  4,  sets  of  data  were  taken  in  which  L,  F,  P,  I  and  D 
are  constant  while  A  and  the  current  varied.  Also  readings  were  taken 
for  A,  V,  P,  t  and  D  constant  while  L  and  the  current  varied. 

A  total  of  thirty-six  plates,  each  containing  four  or  five  curves  were 
obtained  for  the  four  cells.  On  account  of  the  similarity  of  the  large 
number  of  curves  and  data  taken  only  representative  curves  will  be 
given  for  potassium  cell  number  four. 

CURVES. 

A  in  cm2,  represents  the  area  of  metal  illuminated. 
L  in  candle  feet  represents  the  intensity  of  illumination. 
t  in  °  C.  the  temperature  of  the  cell. 

P  in  mm.  mercury  represents  the  pressure  of  the  hydrogen  gas. 
D  in  cm.  represents  the  distance  between  the  electrodes. 
F  in  volts  represents  the  potential  difference  between  electrodes. 
d  in  mm.  represents  the  galvanometer  deflections. 

CRITICAL  VOLTAGE  AND  CURRENT. 

It  was  found  that  when  the  voltage  was  applied  to  the  cells,  it  could 
be  increased  to  a  certain  definite  maximum  value  before  a  deflection  of 
the  galvanometer  was  noticeable  when  the  light  was  not  acting.  If  this 
voltage  was  exceeded  by  an  amount  hardly  readable  on  the  voltmeter  a 
deflection  of  the  galvanometer  resulted.  Furthermore,  if  the  light  was 
permitted  to  act  and  the  voltage  applied,  equal  to  the  maximum  value 
determined  as  stated  above,  a  definite  deflection  of  the  galvanometer  was 
produced;  and,  when  the  light  was  suddenly  turned  off  the  galvanometer 
deflection  always  became  zero.  However,  if  this  maximum  value  of  the 
voltage  were  exceeded  and  the  light  turned  off,  the  deflection  of  the 
galvanometer  was  decreased  but  never  became  zero. 

This  voltage,  therefore,  represents  the  maximum  which  may  be  applied 
to  the  cell,  in  this  particular  case,  and  at  the  same  time  have  the  ionization 
current  produced  only  by  the  action  of  light.  This  value  of  the  voltage 
I  shall  call  the  "critical  voltage,"  and  the  corresponding  current  the 
"critical  current"  for  this  particular  condition  of  the  photo-electric 
cell.  The  critical  voltage  and  the  critical  current  taken  together  give  a 
definite  criterion  for  determining  the  best  conditions  for  sensitiveness. 
When  the  critical  current  is  a  maximum  and  the  critical  voltage  is  a 


VOL.  I 
No.  4. 


SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS. 


279 


minimum,  then  the  most  sensitive  conditions  obtain.     Therefore,  the 

critical  voltage  and  the  critical  current  are  given  in  the  data  and  shown 

by  the  vertical  lines  as  for  example  ab  in  Fig.  3.     If  the  voltage  is  increased 

beyond  the  critical  value,  when  the  cell  is  in  the  dark,  the  current  will 

increase  suddenly,  so  that  it  cannot  be  measured  with  the  galvanometer. 

This  indicates  that  the  sparking 

voltage  is  not  much  greater  than 

the  critical  voltage.     Some  phys-     m.  " 

ical  results,  chosen  from  a  large     .|  ^ 

number  of  observations  are  given     J! 

3" 
fr. 


t 


in  Figs.  3  to  17.  Four  groups  of 
curves  will  be  given.  In  the  first 
group,  Figs.  3  to  10,  relating  to 
a  potassium  cell  before  forma- 
tion of  the  hydride,  the  two 
most  important  independent  va- 
riables, the  electrode  distance  and 
the  gas  pressure  are  studied. 
The  same  holds  for  the  second 
group  of  curves,  Figs.  11-15, 
which  however  have  been  taken 
after  the  formation  of  the  hy- 
dride. The  variation  of  the  area  illuminated  is  represented  in  Fig.  16, 
and  the  variation  of  the  intensity  of  illumination  in  Fig.  17. 


Voltage  on  Metal. 

Variation  of  electrode  distance  reading'from 
left  to  right  0.5-1-2-3  cm.  Gas  pressure  5  mm. 
Before  forming. 

-    Fig.  3. 


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Voltage  on  Metal. 

Variation  of  electrode  distance  reading  from  left  to  right  0.5-1-2-3  cm.      Gas  pressure  2  mm. 
Before  forming.     A  =  4.36  cm'.     L  -  0.22  C.f.     /  =  26°  C. 
Fig.  4. 

The  following  remarks  may  be  made  on  curves  Figs.  3-10.     The 
illuminating  voltages  are  in  the  order  of  the  values  of  D. 


280 


J.  G.  KEMP. 


\ SECOND 
[SERIES. 


Fig.  3.  The  critical  voltage  for  D  =  0.5  cm.  is  the  smallest,  while  the 
critical  current  for  D  =  i.o  cm.  is  the  largest;  therefore,  the  best  condi- 
tion for  this  pressure  is  for  some  value  of  D  between  I  and  2  cm. 


60 

Jsc 


19O         *Ml         260        000        J40 

Voltage  on  Metal. 

Variation  of  electrode  distance  read- 
ing from  left  to  right  1-0.5-2-3  cm. 
Gas  pressure  1  mm.  Before  forming. 
A  -  4.36  cm».  L  =  0.22  C.f.  7  = 
26°  C. 

Fig.  5. 


soo       s  o 


Voltage  on  Metal. 

Variation  of  electrode  distance  reading 
from  left  to  right  0.5-1-2-3  cm.  Temp, 
salt  and  ice  bath.  Gas  pressure  3  mm.  Be- 
fore forming.  A  =  4.36  cm2.  L  =  0.22  C.f. 
t  =  20°  C. 

Fig.  6. 


Fig.  4.  The  order  of  the  illuminating  voltages  is  the  same  as  that 
for  values  of  D.  The  critical  voltage  for  D  =  0.5  cm.  is  the  smallest 
and  the  critical  current  is  the  largest;  therefore,  the  best  conditions  for 
sensitiveness  are  shown  by  this  curve. 

Fig.  5.     The  order  of  the  illuminating  voltages  is  not  the  same  as  that 


Voltage  on  Metal. 

Variation  of  electrode  distance  reading  from  left  to  right  0.5-1-2-3  cm.     Temp.  0°  C.     Gas 
pressure  3  mm.     Before  forming.     A  =  4.36  cm2.     L  =  0.22  C.f.     t  —  0°  C. 

Fig.  7. 


VOL.  I.I 
).4.  J 


No. 


SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS. 


28l 


for  values  of  D.  The  curve  for  D  —  0.5  cm.  lies  between  curves  for 
D  =  i.o  cm.  and  D  =  2.0  cm.  The  curve  D  =  i.o  cm.  shows  best 
conditions  for  sensitiveness. 


~SOO 


sic 


Voltage  on  Metal. 

Variation  of  electrode  distance  reading  from  left  to  right  0,5-1-2-3  cm.     Temp.  38°  C.     Gas 
pressure  3  mm.     Before  forming.     A  =  4.36  cm2.     L  =  0.22  C.f.     t  -  38°  C. 

Fig.  8. 

Fig.  6.  The  order  of  the  illuminating  voltages  is  regular.  The  con- 
ditions of  sensitiveness  are  much  better  as  represented  in  curve  for 
D  =  2.0  cm. 


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Voltage  on  Metal. 

Variation  of  gas  pressure  reading  from  left  to  right  2- 
1-3-5-8  mm.     Electrode  distance  1  cm.     Before  form- 
ing.    A  =  4.36  cm*.     L  =  0.22  C.f. 
Fig.  9. 


Voltage  on  Metal. 
Variation  of  gas  pressure  read- 
ing from  left  to  right  2-3-1-5-8 
mm.  Electrode  distance  0. 5  cm. 
Before  forming.  A  =  4.36  cm1. 
L  =  0.22  C.f. 

Fig.  10. 


Fig.  7.  The  order  of  the  illuminating  voltages  is  regular.  The  best 
conditions  of  sensitiveness  are  represented  by  a  curve  that  would  lie 
between  curves  for  D  =  0.5  cm.  and  D  =  i.o  cm. 


282 


J.  G.  KEMP. 


[SECOND 

[SERIES. 


Fig.  8.  The  order  of  the  illuminating  voltages  is  regular.  The  best 
conditions  for  sensitiveness  are  represented  by  a  curve  which  will  lie 
between  curves  for  D  =  i.o  cm.  and  D  =  2.0  cm. 


Voltage  on  Metal. 

Variation  of  electrode  distance  reading  from  left  to  right  0.5-1-2  cm.     Gas  pressure  10  mm. 
After  forming.     A  =  4.36  cm2.     L  =  0.22  C.f.     t  =  24°  C. 

Fig.  11. 

Fig.  9.  The  curve  for  P  =  i.o  mm.  lies  between  curves  P  =  2.0  mm. 
and  P  =  3.0  mm.,  showing  that  the  critical  pressure  for  minimum 
illuminating  voltage  is  in  the  region  of  2  mm.  The  best  conditions  of 
sensitiveness  are  represented  by  a  curve  which  lies  between  curves  for 
P  =  3.0  mm.  and  P  =  5.0  mm. 


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Voltage  on  Metal. 

Variation  of  electrode  distance  reading  from  left  to  right.     0.5-1-2-3  cm.     Gas  pressure  3  mm. 
After  forming.     A  =  4.36  cm'.     L  =  0.22  C.f.     t  =  25°  C. 

Fig.  12. 

Fig.  10.     The  curve  for  P  =  i.o  mm.  lies  between  curves  for  P  =  3.0 
mm.  and  P  =  5.0  mm.     This  indicates  that  the  critical  pressure  at 


VOL.  I.I 
No.  4.  J 


SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS. 


which  the  illuminating  voltage  is  a  minimum  lies  in  the  region  of  P  =  2.0 
mm.  The  best  conditions  for  sensitiveness  are  represented  by  a  curve 
which  lies  between  curves  for  pressure  between  2  and  3  mm. 


. 


Voltage  on  Metal. 

Variation  of  electrode  distance  reading  from  left  to  right  0.5-1-2-3  cm 
After  forming.     A  =  4.36  cm2.     L  =  0.22  C.f. 

Fig.  13. 


Gas  pressure  2  mm, 
26°  C. 


The  next  set  of  figures,  n  to  15,  represent  values  observed  after  the 
formation  of  the  hydride.  The  following  notes  may  be  made. 

Fig.  II.  The  order  of  illuminating  voltages  is  regular.  The  best 
conditions  for  sensitiveness  are  shown  by  curve  for  D  =  0.5  cm. 


Voltage  on  Metal. 

Variation  of  gas  pressure  reading  from  left  to  right  1-2-3-5-10  mm.     Electrode  distance 
1  cm.     After  forming.     A  =  4.36  cm2.     L  =  0.22  C.f. 

Fig.  14. 

Fig.  12.  The  order  of  illuminating  voltages  is  regular.  The  best 
conditions  for  sensitiveness  are  shown  by  curve  for  D  =  0.5  cm. 

Fig.  13.  The  order  of  illuminating  voltages  is  regular.  The  best 
conditions  for  sensitiveness  are  shown  by  a  curve  which  lies  between 
curves  for  D  =  0.5  cm.  and  D  —  i.o  cm. 


284 


J.  G.  KEMP. 


[SECOND 

[SERIES. 


Fig.  14.  These  curves  show  conditions  of  sensitiveness  for  different 
pressures  and  D  =  i.o  cm.  The  curve  representing  best  conditions  for 
sensitiveness  lies  near  the  curve  for  P  =  3.0  mm. 


Voltage  on  Metal. 

Variation  of  pressure  reading  from  left  to  right  2-1-3-5-10  mm.     Electrode  distance  0.5  cm. 
After  forming.     A  »  4.36  cm2.     L  =  0.22  C.f. 

Fig.  15. 


Fig.  15.  The  curves  show  the  conditions  for  sensitiveness  for  different 
pressures  and  D  =  0.5  cm.  The  curve  representing  best  conditions  for 
sensitiveness  lies  near  the  curve  for  P  =  3.0  mm. 


o  * 


Area  of  Metal  Illuminated. 

Variation  of  area  of  metal  illuminated.  Intensity  of  illumination  0.22  C.f.  Gas  pressure 
2  mm.  Electrode  distance  0.5  cm.  Voltage  on  metal  reading  from  top  downward  295,  294, 
293  volts. 

Fig.  16. 


The  curves  of  Fig.  16  show  the  variation  of  area  of  metal  illuminated. 
The  form  of  these  curves  indicates  that  variations  in  small  areas  illumi- 


VOL.  Li 
No.  4.  J 


SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS. 


285 


nated  produce  large  changes  in  the  current,  and  variations  in  large  areas 
illuminated  produce  small  changes  in  the  current.  These  facts  show 
that  there  is  a  maximum  area  of  illumination  for  this  particular  type  of 
photo-electric  cell  which,  if  exceeded,  will  not  increase  the  sensitiveness. 
The  form  of  the  curve  should  be  a  straight  line  if  the  electric  field 
were  uniform,  the  surface  conditions  uniform,  with  no  reflection  of  the 
light,  and  no  shadow  caused  by  the  electrode.  In  this  cell  the  above 
conditions  were  not  fulfilled,  therefore  the  form  of  the  curve  is  not  a 
straight  line.  It  follows  finally  a  system  of  curves  showing  the  variation 
of  the  intensity  of  illumination  for  three  different  voltages,  the  observa- 


Intensity  of  Illumination  =  .K/P. 

Variation  of  intensity  of  illumination.     Electrode  distance  0.5  cm.     Voltage  on  metal  reading 
from  top  downward  366,  365,  364  volts.     After  forming. 

Fig.  17. 

tions  are  taken  after  the  forming  of  the  cell.  In  Fig.  17  showing  variation 
of  current  with  intensity  of  illumination  for  P  =  5  mm.  the  points  for 
the  smaller  voltages  lie  more  nearly  on  a  straight  line.  The  largest  error 
in  the  intensity  for  the  point  farthest  from  the  line  is  7  per  cent,  of  .15 
C.f.  or  .01  C.f.  The  points  for  smaller  intensities  show  much  smaller 
deviations  than  those  for  larger  intensities.  The  higher  voltages  applied 
caused  unsteadiness  of  the  current,  hence,  the  galvanometer  deflections 
are  liable  to  larger  errors. 


BEST  CONDITIONS  FOR  SENSITIVENESS. 

By  comparing  the  values  for  the  critical  voltages  and  currents  ob- 
tained from  the  curves  the  best  sensitive  conditions  may  be  selected. 

A  table  of  these  values  is  given  below  for  both  before  and  after  forming 
the  hydride  on  the  surface  of  the  metal. 


286 


J.  G.  KEMP. 


f SECOND 
L  SERIES. 


TABLE  TO  SHOW  BEST  CONDITIONS  FOR  SENSITIVENESS. 

V  =  critical  voltage. 

/  =  critical  current  in  galvanometer  deflections. 
D  —  best  distance  between  electrodes  in  cms. 
P  =  best  pressure  in  mm. 

Before  Forming  Metal. 


Figure. 

V 

/ 

D 

p 

3 

460  to  527 

16  to  28 

1  to  2 

5.0 

4 

304 

26 

0.5 

2.0 

5 

349  to  366 

6  to  9 

1  to  2 

1.0 

6 

454 

8 

2 

31 

7 

335  to  396 

10  to  45 

0.5  to  1.0 

32 

8 

383  to  431 

7  to  11 

1  to  2 

33 

9 

387  to  460 

28  to  29 

1 

3  to  5 

10 

304  to  324 

26  to  32 

0.5 

2  to  3 

After  Forming  Metal. 


11 

479 

280 

0.5 

10 

12 

331 

off  scale 

0.5 

3 

13 

296  to  331 

123  to  190 

0.5  to  1.0 

2 

14 

374 

203 

1 

3 

15 

331 

off  scale 

0.5 

3 

By  inspection  of  the  table  above,  it  is  seen  that  the  best  conditions  for 
sensitiveness  before  forming  are  about 

V  =  300  volts. 
D  =  0.5  cm. 
P  =  2  to  3  mm. 
/  =  25°  C. 

And  the  best  conditions  for  sensitiveness  after  forming  are  about 

V  =  330  volts. 
D  =  0.5  cm. 
P  =  3  mm. 
/  =  25°  C. 

The  cell  is  about  100  times  more  sensitive  after  forming  than  before 
forming. 

THEORETICAL  DEDUCTION  OF  MEASUREMENT  OF  INTENSITY  OF 

ILLUMINATION. 

If  the  intensity  of  illumination  varies  directly  with  the  current  for 
very  small  intensities,  then  it  is  possible  to  calculate  the  intensity  meas- 
urable with  an  instrument  of  given  sensibility. 
1  About  —  20°  C.  salt  and  ice. 

20°C. 

» 38°  C. 


No"4L]  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS.  287 

From  Fig.  18  below  it  is  seen  that  for  the  curve  of  366  volts, 

d      130 
tan  6  =  -  =  -  -  =  0.65, 

5         200 

or 

d 


S  = 


tan  6      0.65 


Fig.  18. 
cd  —  I  current  flowing, 

c  =  3.78  X  IO"10  amp.  per  mm.  deflection, 
d  =  0.65  X  3-78  X  i^i  mm" 


but 

K 


and  for  particular  values  of  5  =  200,  and  I2  —  (100  cm.)2, 
K  =  SI2  =  200  X  (ioo)2  cm.  =  2  X  io6  cm. 


S  =  — „ ,     or    / 

Substitute  value  of 


2JX  I0<5      _     7  =      {2  X  io6 

\       5 


5  =  — 


0.65  X  378  X  io-10 
in  eq.  above,  then 

|2X  io6  X  0.65  X  3.78  X  IP"10  _      f  4.9  X  io~4 
=  \  I  =\      ~T 

By  means  of  an  electrometer  a  current  /  =  io~12  can  be  measured. 
Substituting  this  value  of  I  in  the  equation  above,  then, 


-4 


4.9  X  io-4 

=12  —  =  2-21  *  io4  cm.  or  221  meters, 


the  distance  the  2.47  c.p.  lamp  could  be  removed  from  the  cell  and  still 
be  detected.  By  means  of  a  tilted  electroscope  a  current  /  =  io~15 
amperes  can  be  measured. 

Substitute  this  value  in  the  equation, 


=  \ 


15  ^4-9  X  IQl1  =  7  X  io5  cm.  or  7  kilometers  or  4.3  miles. 

The  2.47  c.p.  lamp  could  be  detected  by  means  of  an  electroscope  at  a 
distance  of  4.3  miles.  To  detect  a  candle  instead  of  the  2.47  c.p.  lamp 
at  4.3  miles  distance  by  means  of  the  tilted  electroscope  of  io~15  sensi- 
bility the  distance  could  be  as  follows  :  Since  the  intensities  of  illumination 
of  cell  must  be  the  same,  then, 


288  J.  G.  KEMP. 


[SERIES. 


(4-3)2      'P '  v<»47 

Professor  Joel  Stebbins,1  of  the  University  of  Illinois,  in  his  work  on 
measuring  the  variation  of  intensity  of  illumination  of  the  variable  stars 
Algol  and  others  used  a  selenium  cell.  It  is  possible  to  detect  a  candle 
at  a  distance  of  500  meters,  or  0.3  mile,  with  such  a  selenium  cell. 

The  equation  for  the  distance  at  which  this  potassium  cell  is  sensitive 
when  the  current  is  measured  with  a  tilted  electroscope  is 


and  for  some  other  distance  it  is 

k 


m 

=  V72' 


/I2  /2 

yr  =  — ,     /i  =  7  X  io5  cm.,     k  =  5  X  io4  cm., 

then 

/!2      49  X  io10 

v  =  25  x  io8  ==2X     approximately- 

Thus  it  is  seen  that  the  potassium  cell  is  about  two  hundred  times  more 
sensitive  than  the  selenium  cell. 

ENERGY  REQUIRED  TO  PRODUCE  AN  ION. 

To  produce  an  ion  a  certain  minimum  amount  of  energy  is  required. 
This  energy  is  that  required  to  draw  an  electron  out  of  an  isolated  mole- 
cule against  the  force  of  attraction  of  the  positive  charge  of  the  molecule. 
Let  Ri  be  the  radius  of  the  molecule,  e\,  the  positive  charge,  e2,  the  negative 
charge  of  electron.  If  the  electron  be  displaced  a  distance  dR  the  work 
done  will  be 

**-%**. 

The  total  energy  required  to  draw  an  electron  outside  of  the  influence  of 
the  positive  charge  is 

W  =    I     -fa  dR  =  -jr-  units  of  work. 

ei  =  e2  =  4.67  X  io-10  E.S.U. 
Rl  —  io~8  cm.  for  hydrogen. 


1  Astrophysical  Journal,  October,  1911. 


SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS.  289 

the  minimum  amount  of  energy  required  to  draw  an  electron  from  an 
isolated  molecule  of  hydrogen  or  to  produce  a  hydrogen  ion. 

For  an  isolated  molecule  it  is  necessary  to  withdraw  the  electron  to  an 
infinite  distance  from  the  center.  If  the  molecule,  however,  is  in  an 
electric  field  the  force  of  attraction  between  the  molecule  and  the  electron 
is  zero  at  a  distance  say  R%  from  the  center.  The  effect  of  the  electric 
field  tends  to  decrease  the  energy  required  to  withdraw  the  electron  on 
one  side  of  the  molecule  (with  references  to  the  direction  of  external 
electric  field)  while  that  on  the  opposite  side  is  increased. 

Let  Fig.  19  represent  the  molecule  of  radius  Rii  H  is  the  direction  of 
the  external  field  in  the  direction  of  motion,  Oa,  of 
the  electron.  Let  Rz  be  the  distance  beyond  which 
the  electric  attraction  between  the  positive  charge 
of  the  molecule  and  the  electron  is  zero,  The  work 
required  to  withdraw  the  electron  beyond  the  influ-  Fig.  19. 

ence  of  the  molecule  is 


W  =  J      -j^dR  = 

but  e\  —  ei  =  e\  and  it  is  reasonable  to  assume 


Substituting  the  values  for  R\  and  e, 

W  ==*£££*= -urx --.P. 

Thus  the  value  of  W  in  calculation  (2)  is  three  fourths  that  in  calcula- 
tion (i).  Hence  2.18  X  icr11  ergs  is  not  the  minimum  value. 

The  minimum  amount  of  energy  required  to  produce  an  ion  by  col- 
lision can  be  determined  roughly  from  the  data  taken  in  this  investigation. 
For  the  conditions  of  this  work  the  minimum  energy  is  W  =  Eel,  where 
E  is  the  potential  gradient,  or  electric  force,  e  is  the  charge  of  a  negative 
ion  or  electron,  and  /  is  the  mean  free  path  of  an  ion.  The  force  E  can 
be  determined  roughly  as  follows:  The  voltage  applied  to  the  electrodes 
of  the  cell  necessary  to  produce  velocities  high  enough  to  cause  ionization 
by  collision,  is  obtained  from  the  ionization  curves.  This  voltage  is 
shown  very  distinctly  at  the  point  on  the  curve  where  the  ordinate  or 
current  shows  an  increase  after  the  saturation  state  has  been  reached. 
Let  V  be  this  voltage  taken  from  the  curve,  and  let  D  be  the  distance 
between  the  electrodes.  Then, 

3Qp£>  . 
E=   —  mE.S.U. 


290  J.  G.  KEMP. 

(a)   FIRST  ASSUMPTION  REGARDING  MEAN  FREE  PATH  OF  ELECTRONS. 
Assuming  that  the  negative  ions  or  electrons  and  the  molecules  of  the 
hydrogen  gas  act  as  a  mixture  of  two  gases,  the  equation  of  the  mean  free 
path  given  by  Maxwell  in  the  kinetic  theory  of  gases  is 

h- r—       .'     .. 

—  /YYl\ 

^>  YHz 

for  the  electrons, 


for  hydrogen  molecules. 

For  an  electron  an  the  diameter  of  the  sphere  of  action  when  two  elec- 
trons collide  is  practically  zero.  But  cri2  the  diameter  of  the  sphere  of 
action  when  an  electron  collides  with  a  molecule  of  hydrogen  is  assumed 
equal  to  the  radius  of  the  molecule  or  icr8  cm. 

m\  is  the  mass  of  an  electron  equal  to  8.8  X  io~28  grams. 

mz  is  the  mass  of  a  hydrogen  molecule  equal  to  1.6  X  io~24  grams. 

mi       8.8  X  io~28 


1.6  X  io~: 


24 


5.5  X  io~4  gram 


This  value  is  negligible  in  comparison  with  unity  or  ^1  I  -\  --  1.     The 
equation  for  the  mean  free  path  of  the  electron  is 

n  =      M      i)  cm. 


In  this  equation  Nz  is  the  number  of  molecules  per  cubic  centimeter. 
From  the  kinetic  theory  of  gases  Nz  may  be  calculated.     PV  =  RT,  the 
gas  law,  which  becomes  PV  =  \L  —  \N'  =  $mC2. 
Where  L  is  the  average  total  kinetic  energy. 

Nf  is  the  number  of  molecules  in  volume  V. 

C2  is  the  square  of  average  velocities  of  molecules. 

^mCz  =  aT,  where  a  is  the  universal  constant. 

PV  =  %N'aT,  or 

P  =  %NaT  for  unit  volume. 

N  =  ^-PjaT  the  number  of  molecules  per  unit  volume 

3  13.6  X  980^ 

=  2T^T^r;/zlsmcm- 

Suppose  T  =  27  +  273  =  300  for  this  work. 


VOL.^I.]  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS.  29 1 

Substitute  this  value  for  N*  in  the  expression  for  the  mean  free  path. 

I _  965  X  IP"5 

T  X  33  X  io16fc  X  io-16  "  h 

Applying  the  equation  W  =  Eel, 

e  =  4.67  X  io-10  E.S.U. 

E  =  -      -  E.S.U. 
30o£ 

l    =  965  X  io-5 

For  h  =  0.5  cm.,  D  =  i.o  cm.,  V  =  330  volts, 

4.67  X  io-10  X  965  X  io-5 

W  =  -  -  =  1.09  X  io~u  ergs. 

300  X  i.o  X  0.5 

An  average  of  ten  determinations  gave  1.05  X  io~u  ergs  for  the  minimum 
energy  required  to  produce  an  ion  in  hydrogen  by  collision. 

(b)  SECOND  ASSUMPTION  REGARDING  MEAN  FREE  PATH  OF  ELECTRONS. 
If  it  be  assumed  that  the  negative  ions  or  electrons  occupy  no  space  in 
the  gas,  or,  that  the  hydrogen  gas  acts  as  though  the  electrons  were  not 
present,  then  the  value  of  the  mean  free  path  is  the  same  as  that  of  the 
molecules.  That  is, 


685   X    I O-5 

4  -        —h-   -  cm. 

For  h  =  0.5  cm.,  D  =  i.o  cm.,  V  =  330  volts, 
4.67  X  io-10  X  685  X  IP"5  X  330 
W  :  300  X  0.5  -  -  '7°  X 

About  35  per  cent,  decrease  from  1.05  X  io~11  ergs. 

(c)  THIRD  ASSUMPTION  REGARDING  MEAN  FREE  PATH  OF  ELECTRONS. 
By  using  the  assumption  that  the  mean  free  path  of  the  electrons  is 
4^/2  times  mean  free  path  of  the  hydrogen  molecules,  as  Bishop1  did, 
the  following  results  are  obtained. 

,  /-  ^42 i,36oXiQ-5 

=  4v/2/2  -  T33  x   IQ_16A  x  4 

w  ,  IJTjOcgLX  1,360  X  io-5        V '  IQ_15  V 

300  Dh  Dh 

1  PHYSICAL  REVIEW,  325,  November,  1911. 


292  J-  G-  KEMP. 

For  P  =  0.3  cm.,  D  =  i.o  cm.,  V  =  260  volts, 

260 

W  =  21  X  io~15  — — =  1.82  X  io-n  ergs. 

I  X  0.3 

An  average  of  10  calculations  gives  1.77  X  io~u  ergs. 

To  recapitulate,  the  values  determined  above  and  those  by  other 
investigators  are: 

1.  For  an  isolated  molecule  the  theoretical  value  is  2.18  X  io~u  ergs. 

2.  For  a  molecule  in  an  electric  field  the  theoretical  value  is  1 .63  X  io~n 
ergs. 

3.  The  average  of  ten  values  determined  from  the  data  in  accordance 
with  the  first  assumption  is  1.05  X  io~~n  ergs. 

4.  The  value  determined  in  accordance  with  the  second  assumption  is 
0.70  X  io~n  ergs. 

5.  The  average  of  ten  values  determined  in  accordance  with  the  third 
assumption  is  1.77  X  io~u  ergs. 

6.  Bishop  obtained  a  value,  by  a  method  similar  to  that  used  in  this 
work  and  in  accordance  with  the  third  assumption  used  in  the  fifth 
determination,  1.58  X  io~u  ergs. 

7.  Rutherford1  determined  the  energy  required  to  produce  an   ion 
by  the  alpha  particle.     His  value  is  2.7  X  io~n  ergs. 

8.  Geiger,2  and  later  Taylor,3  using  the  same  method,  obtained  about 
5  X  io~11  ergs,  and  other  investigators  obtained  values  even  as  large  as 
10  X  io~u  ergs. 

In  the  method,  based  on  the  ionizing  power  of  alpha  particles,  it  is 
assumed  that  their  loss  of  kinetic  energy  is  entirely  transformed  into 
energy  of  ionization,  and  that  the  decrease  of  the  kinetic  energy  over  a 
certain  range  divided  by  the  total  numbers  of  ions  produced  gives  the 
energy  required  to  produce  one  ion.  Since  a  part  of  the  kinetic  energy 
of  the  alpha  particle  increases  the  average  kinetic  energy  of  the  gas 
without  producing  ions,  the  ionizing  energy  is  taken  too  large  and  the 
energy  required  to  produce  an  ion  is  necessarily  too  large. 

Value  number  (i)  represents  the  minimum  energy  required  to  produce 
an  ion  when  a  molecule  is  isolated.  This  value  is  much  larger  than  that 
for  a  molecule  in  an  electric  field.  Rutherford's4  determination  is  much 
nearer  the  value  number  (i)  than  any  of  the  others. 

Bishop's  determination  is  very  close  to  the  value  number  (2),  while  my 
determination  of  the  ionizing  energy  is  slightly  larger.  Since  the  assump- 
tion regarding  the  mean  free  path  in  numbers  5  and  6  are  the  same,  and 

1  Radio-Activity,  second  edition,  p.  552. 
1  Proc.  Royal  Soc.,  Vol.  82,  p.  486,  1909. 
8  Phil.  Mag.,  p.  670,  April,  1912. 
4  Radio-Activity,  second  edition,  p.  552. 


Na'4L]  SENSIBILITY  OF  PHOTO-ELECTRIC  CELLS.  293 

these  values  differ  very  slightly  from  the  theoretical  value  number  (2), 
it  indicates  that  the  assumptions  made  are  not  far  from  the  truth. 

Owing  to  lack  of  time  and  space  an  exact  determination  of  the  minimum 
energy  required  to  produce  an  ion  by  collision  is  impossible;  in  the  near 
future,  however,  it  is  hoped  that  this  can  be  done  with  the  data  already 
in  hand. 

A  design  has  been  made  for  a  sensitive  photo-electric  cell  for  photo- 
metric work  in  astronomy.  It  is  expected  to  get  a  cell  which  will  be 
sensitive  enough  to  use  instead  of  the  erratic  selenium  cell  now  used. 

SUMMARY  AND  CONCLUSIONS. 

The  following  facts  are  established  by  this  investigation  for  this  type 
of  photo-electric  cell. 

1.  Owing  to  the  low  melting  temperature  of  caesium  the  use  of  this 
metal  in  photo-electric  cells  for  photometric  use  is  very  impractical. 

2.  The  temperature  at  which  it  is  best  to  operate  a  potassium  cell  is 
about  25°  C. 

3.  Cooling  the  potassium  cell  much  below  25°  C.  does  not  increase  its 
sensitiveness. 

4.  The  sensibility  of  a  potassium  cell  can  be  increased  more  than  100 
times  by  the  process  of  forming  the  hydride  surface. 

5.  The  distance  between  the  electrodes  for  best  sensitiveness  is  about 
0.5  cm. 

6.  The  hydrogen  gas  pressure  at  which  the  cell  is  most  sensitive  lies 
between  2  and  3  mm.  of  mercury. 

7.  The  potential  difference  applied  to  the  electrodes  for  most  sensitive 
conditions  is  about  330  volts. 

8.  The  minimum  energy  required  to  produce  an  ion  by  collision  was 
calculated  from  the  data  and  found  to  be  of  the  order  1.77  X  io~u  ergs, 
while  the  theoretical  value  determined  is  1.63  X  io~n  ergs. 

9.  Assuming  that  the  straight  lines  obtained  which  show  the  relation 
between  current  and  intensity  of  illumination  hold  for  exceedingly  small 
intensities,  then  by  using  a  tilted  electroscope  of  sensibility  io~15  amperes, 
a  candle  could  be  detected  at  a  distance  of  2.7  miles.     This  indicates  that 
it  is  highly  probable  that  a  photo-electric  cell  could  be  used  in  astro- 
photometric  work. 

The  author  takes  great  pleasure  in  acknowledging  his  indebtedness  to 
Professor  A.  P.  Carman  for  the  facilities  for  this  investigation,  and  to 
Professor  Jakob  Kunz,  both  for  his  general  supervision  of  the  work  and 
for  many  valuable  suggestions. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS. 


The  Use  of  Sounding-Boards 
in  an  Auditorium 


Reprinted  from  The  Brickbuilde* 
June,  1913 


The   Use  of  Sounding-Boards  in  an 

Auditorium. 

BY  F.   R.  WATSON. 
Assistant  Professor  of  Physics,  University  of  Illinois. 


OOUNDING-BOARDS  are  well 
O  known  because  of  their  use  in  audi- 
ence halls  where  the  acoustical  proper- 
ties are  unsatisfactory.  Thus  many 
churches  are  found  equipped  with  this 
device  with  the  expectation  that  the 
acoustics  will  be  made  better.  Because 
of  this  common  use  the  author  has  been 
led  to  test  sounding-boards  of  different 
forms,  to  determine,  if  possible,  their 
value  in  bettering-  the  acoustics  of  an 
auditorium. 

The  experiments  were  carried  out  as 
a  part  of  a  more  complete  investigation 
of  the  acoustical  properties  of  the  audi- 
torium of  the  University  of  Illinois. 
This  auditorium  is  shaped  nearly  like  a 
hemisphere  with  several  large  arches 
and  recesses  to  break  the  regularity  of 
the  inner  surface.  (See  Figs.  I  and 
IV.)  The  original  plans  of  the  archi- 
tect were  curtailed  because  the  amount 
of  money  appropriated  for  the  construc- 
tion of  the  building  was  insufficient  for 
the  purpose.  The  interior  of  the  hall 
was  built  absolutely  plain  with  no  break- 
ing up  of  the  smooth  wall  surfaces,  and 
no  furnishings  were  provided  in  the 
shape  of  carpets  or  curtains.  The 
acoustical  properties  proved  to  be  unsat- 
isfactory. A  reverberation,  or  undue 
prolongation  of  the  sound,  existed.  In 
addition,  echoes  are  set  up  because  of 
the  large  size  of  the  room  and  because 
of  the  position  and  form  of  the  walls. 

A  diagnosis  of  the  acoustics  was  made. 
The  time  of  reverberation  was  deter- 
mined by  Sabine's  method*  to  be  a  little 


more  than  six  seconds.  The  echoes  were 
located  by  tracing  out  the  paths  taken 
by  the  sound.  This  was  done  by  means 
of  an  arc-light  backed  by  a  parabolic 
reflector. t  The  arc  gave  out  sound 
waves  in  addition  to  the  light ;  the  two 
sets  of  waves  traveling  together,  so  that 
by  noting  where  the  light  struck  a  wall, 
an  observer  could  ' '  see  ' '  where  the 
sound  traveled.  The  echoes  were  finally 
eliminated  by  placing  canvas  curtains  so 
as  to  break  up  the  sound  waves  that 
produced  the  trouble. 

It  occurred  to  the  author  during  the 
course  of  the  investigation  that  sound- 
ing-boards might  be  helpful  in  curing 
the  echoes.  Several  forms  of  boards 
were  used.  A  flat  board,  about  5  feet 
square,  inclined  at  an  angle  above  the 
head  of  the  speaker,  produced  but  little 
effect.  A  canvas  sheet,  about  12  by  20 
feet,  similarly  placed,  was  also  unsatis- 
factory, although  speakers  said  they 
could  talk  better  under  it  than  out  in  the 
open.  Sounding-boards  were  then'used 
of  a  parabolic  shape,  and  these  produced 
a  pronounced  effect. 

The  sounding-board,  or  more  prop- 
erly, the  reflecting  board,  was  set  up 
at  one  side  of  the  platform,  after  the 
manner  of  the  pulpits  in  Episcopal 
churches.  (Fig.  II.)  The  shape  of  the 
reflector  was  a  quarter  section  of  a  pa- 
raboloid of  revolution  with  the  axis 
nearly  horizontal .  The  frame  was  made 
of  wood,  and  faced  on  the  under  side 
with  hard  plaster  on  wire  lath.  The 
finished  reflector  is  shown  in  Fig.  III. 


*W.  C.  Sabine,  "Architectural  Acoustics,"  Amer- 
ican Architect,  1900. 


t  F.  R.  Watson,    "  Echoes  in  an   Auditorium," 
Physical  Review,  Vol.  32,  page  231,  1911. 


The  results  obtained 
were  pronounced. 
Previous  calculations 
showed  that  the 
sound  would  be  di- 
rected in  such  a  way 
as  to  confine  the 
echoes  to  a  small  sec- 
tion of  the  audience. 
A  canvas  of  the  audi- 
tors showed  this  to  be 
the  case.  Echoes 
were  reported  in  the 
section  expected,  but 
the  remainder  of  the 
audience  had  no  such 
trouble. 

Some  time   later 


FIG. 


another  reflector  of  the  same  shape  and 
size  was  made  and  mounted  over  the 
center  of  the  stage.  This  was  done  be- 
cause speakers  regarded  the  raised  pul- 
pit arrangement  on  the  side  of  the  stage 
as  rather  formidable .  This  second  frame 
was  much  lighter  in  weight.  It  was 
constructed  of  small  wooden  rods  in  a 
most  ingenious  way  by  one  of  the 
University  carpenters.  (See  Fig.  V.) 


FIG.  III.   COMPLETED  REFLECTOR. 


CONSTRUCTION  OF  REFLECTOR. 

It  was  faced  with  white  oilcloth  (see 
Fig.  VI)  instead  of  plaster,  since  it  had 
been  found  that  the  oil  cloth  was  a  good 
reflector  of  sound  and  was  much  lighter 
in  weight.  The  result  obtained  by  its 
use  confirmed  the  expectations  as  in  the 
previous  experiment. 

Reflectors  of  this  kind  have  certain 
objectionable  features.  Thus,  if  the 
mouth  of  the  speaker  is  at  the  focus  of  a 
paraboloid,  the  re- 
flected sound  goes  out 
in  a  parallel  bundle 
and  only  a  small  por- 
tion of  the  audience 
gets  the  reenforced 
sound.  This  was 
found  to  be  so  in  the 
two  cases  cited.  Ex- 
periments showed  the 
sound  to  be  confined 
to  the  region  calcu- 
lated. Auditors  in 
this  region  reported 
an  increased  sound, 
while  others  outside 
this  zone  had  no  such 
reenforcement.  To 
remedy  this  short- 


FIG.  V.       FRAMEWORK  FOR  REFLECTOR 

coming"  and  direct  the  sound  to  all  the 
auditors  would  require  a  reflector  of  dif- 
ferent form.  The  results  obtained  indi- 
cate that  this  could  be  done  by  making- 
up  a  modified  parabolic  reflector  to  suit 
the  conditions  of  the  particular  case. 

One  other  defect  is  the  annoyance  to 
the  speaker.  Thus;  if  his  head  is  near 
the  focus  (Figf.  VII),  he  is  in  a  position 
to  get  concentrated  sound  from  the  audi- 
ence, i.e.,  coughing-, 
sneezing:,  rustling  of 
papers,  etc.  With  the 
reflectors  used,  no 
such  annoyance  oc- 
curred. The  two 
gentlemen  who  spoke 
—the  Right  Rever- 
end Bishop  Osborne, 
who  used  the  reflector 
at  the  side  of  the 
stage,  and  Reverend 
Hugh  Black,  who 
used  the  reflector  in 
the  center  of  the  stage 
—  each  expressed  his 
satisfaction  with  the 
reflector  and  reported 
no  annoyance  in 


speaking.  The  steep 
slope  of  the  reflector 
eliminated  any  feel- 
ing of  being  ' '  shut 
in. ' '  A  speaker 
standing-  at  the  focus 
is  not  conscious  of 
the  presence  of  the 
reflector  unless  he 
turns  around  and 
looks  at  it. 

The      advantages 
possessed  by  such   a 
suitably  desigfned  re- 
flector   are     perhaps 
two    in    number . 
First,  it  serves  to  cut 
off  the  sound   which 
passes  to  walls  that  may  produce  acous- 
tical disturbances,  and  second,  to  direct 
this  sound  usefully  to  auditors  at  a  dis- 
tance from  the  speaker.     Both  of  these 
effects  were  obtained  in  the  auditorium 
at  the  University  of  Illinois.     It  is  not 
planned  to  use  the  reflector  at  the  latter 
place,    since,  as  already  indicated,   the 
echoes  can  be  eliminated  by  the  instal- 
lation of  false   walls  in   the   dome.     It 


FIG.  VI.       REFLECTOR  OVER  PULPIT. 


seems  likely  that  such  a  reflector  would 
be  useful  in  a  hall  where  the  walls  could 
not  conveniently  be  modified.  It  would 
be  especially  adapted  for  use  in  churches 


or    halls    where    the    position    of    the 
speaker  is  confined  to  a  small  space.  * 


*  See  Architectural  Review,  Vol.  I,  Plate  LVIII, 
December,  1912. 


FIG.  VII, 


[Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  II.,  No.  i,  July,  1913.] 


ON  THE  BEADED  CHARACTER  OF  THE  CATHODE  RAY  LINE 

AS  REVEALED  BY  INSTANTANEOUS  PHOTOGRAPHS 

TAKEN  AT  SHORT  RANGE. 

BY  CHAS.  T.  KNIPP. 

THE  magnetic  spectrum,  so  called,  of  cathode  rays  has  been  investi- 
gated by  Birkeland,  Strutt,  and  Thomson,1  and  is  generally  con- 
ceded to  be  due  to  the  want  of  uniformity  necessarily  associated  with  the 
use  of  an  induction  coil.     It  was  early  shown  that  similar  effects  may  be 
obtained  by  using  an  electrostatic  instead  of  a  magnetic  field. 

Recently,  while  photographing  at  short  range  the  carriers,  atomic  in 
size,  of  both  positive  and  negative  electricity  that  accompany  the  cathode 
beam,  I  was  impressed  with  the  beaded  character  of  the  cathode  ray  line. 
The  distinctness  and  regularity  of  the  beads  suggested  that  their  origin 
might  possibly  be  other  than  a  want  of  uniformity  that  accompanies  the 
induction  coil  or  static  machine  discharge,  or  other  than  the  presence  of 
secondary  rays. 

APPARATUS  AND  MANIPULATION. 

The  apparatus  employed  was  that  described  in  a  recent  number  of  the 
PHYSICAL  REVIEW.2  The  modifications  necessary  were  slight.  The 
Wehnelt  cathode  was  removed  and  in  its  stead  an  ordinary  aluminum 
cathode  was  suitably  mounted.  The  beam  of  cathode  rays  emergent 
from  the  canal  passed  between  the  nearly  coterminous  magnetic  poles 
and  electrostatic  field  plates  and  fell  upon  the  photographic  plate  beyond. 
This  range  was  about  2  centimeters.  Seed's  lantern  slide  plates  were 
used.  Mounting  and  exposing  a  plate  to  the  action  of  the  rays  was 
briefly  as  follows:  The  circular  plate,  fastened  to  the  movable  brass 
disc3  at  three  points  by  means  of  half  and  half  wax,  was  placed  in  the 
cylindrical  plateholder,  which  in  turn  slipped  into  position  in  the  appa- 
ratus. After  connecting  the  winch  for  turning  the  plate  the  glass 
containing  vessel  was  sealed  and  the  pump  started.  When  the  desired 
degree  of  exhaustion  was  reached,  either  with  or  without  the  aid  of 
charcoal  and  liquid  air,  the  electrostatic  field  was  turned  on  and  the 
discharge  started.  To  get  instantaneous  photographs  it  was  only  neces- 
sary to  rotate  the  plate  while  the  discharge  was  passing. 

1 J.  J.  Thomson,  Conduction  of  Electricity  through  Gases,  2d  ed.,  p.  633. 

2  C.  T.  Knipp,  PHYS.  REV.,  XXXIV.,  March,  1912. 

3  See  Fig.  i  of  article  referred  to  above. 


4°  CHAS.  T.  KNIPP. 

Thus  under  varying  conditions  of  deflecting  fields  (either  magnetic, 
electrostatic,  or  both),  aperture,  vacuum  and  source  of  discharge,  to- 
gether with  varying  conditions  of  resistance,  self-induction,  and  capacity 
in  the  circuit,  photographs  of  great  diversity  were  possible.  The  short 
range  that  the  carriers  traveled  enabled  impressions  to  be  received  and 
recorded  on  the  plate  that  at  greater  distances  would  doubtless  be  lost 
because  of  absorption. 

GENERAL  CONSIDERATIONS. 

The  electrostatic  displacement  of  the  cathode  ray  particle  as  recorded 
by  the  photographic  plate  is  given  by  the  equation 

Ae 
X  -  Irf  (I) 

while  the  magnetic  displacement  is 

Be 

y  =  — ,  (2) 

mv 

where  A  and  B  are  constants  depending  upon  the  strength  of  the  two 
fields  respectively  and  upon  the  geometrical  data  of  the  discharge  vessel. 
From  these  it  follows  that  for  a  given  range  of  velocities  the  greatest 
dispersion  is  to  be  had  when  an  electrostatic  field  is  employed.  If  there 
are  present  carriers  having  a  wide  range  of  velocities,  falling  off  gradually 
from  a  maximum,  then  the  time  exposures  when  either  field  is  employed 
should  appear  on  the  plate  as  a  straight  line  shading  off  gradually  in 
intensity  as  you  recede  from  the  geometrical  or  undeflected  spot.  The 
character  of  the  instantaneous  photographs  will  depend  upon  whether 
the  discharge  is  intermittent  or  not.  In  the  former  case,  the  case  of  an 
induction  coil  discharge,  the  instantaneous  exposures  will  be  similar  in 
shape  and  shading  to  the  time  exposures,  only  much  less  intense.  If, 
however,  the  discharge  is  continuous,  such  as  may  be  had  from  a  high 
potential  storage  battery,  the  instantaneous  exposures  should  reveal 
a  continuous  uniformly  drawn  out  band  similar  in  shading  to  the  time 
exposure  only  much  less  intense.  Uniformity  in  the  direction  of  rotation 
of  the  continuous  band  may  be  expected  only  when  the  plate  is  rotated 
with  uniform  velocity. 

It  would  seem,  then,  that  under  the  conditions  just  stated  this  arrange- 
ment of  apparatus  should  reveal  radiations  that  might  have  their  origin 
in  the  discharge  and  possess  energy  enough  to  affect  a  photographic 
plate,  as  for  instance  (i)  the  presence  of  carriers  due  to  ionization  or 
secondary  effects,  (2)  the  possible  emission  of  group  velocity  electrons 
from  the  surface  of  the  cathode,  or  (3)  group  velocity  electrons  that  may 
have  their  rise  in  the  oscillatory  character  of  the  electric  discharge. 


']  CHARACTER  OF  CATHODE   RAY  LINE.  41 

In  the  first  case,  that  of  ionization,  it  is  reasonable  to  expect  that  the 
photographs  should  show  configurations  that  are  fixed  for  both  the  time 
and  the  instantaneous  exposures,  but  that  would  not  necessarily  be  the 
same  for  a  succeeding  plate,  and  in  general  would  not  follow  a  definite 
law  or  sequence.  In  other  words,  the  instantaneous  photographs  of  the 
cathode  ray  line,  produced  by  say  an  induction  coil  discharge,  might  show 
beads  due  to  ionization  and  secondary  effects,  but  it  is  not  likely  that  the 
spacing  of  these  beads  along  the  line  would  follow  any  definite  sequence 
though  the  spacings  from  instantaneous  photograph  to  instantaneous 
photograph  for  a  given  plate  more  than  likely  would  be  the  same. 

In  the  second  case  if  the  cathode  gave  off  group  velocity  electrons  the 
effect  on  the  plate  should  be  marked — both  for  time  and  instantaneous 
exposures.  Again,  it  does  not  seem  clear  that  any  definite  spacing  of 
the  beads  should  be  expected  though  the  spacing,  whatever  it  might 
have,  would  be  characteristic  of  the  metal.  That  the  cathode  gives  off 
simultaneously  group  velocity  electrons  is  by  no  means  assured,  though 
a  careful  study  of  the  photographs  lends  that  view  some  support. 

Finally  in  the  case  of  group  velocity  electrons  that  have  their  rise, 
when  the  discharge  is  intermittent,  to  the  oscillatory  character  of  the 
discharge  we  can  foretell  quite  accurately  what  the  effect  on  the  photo- 
graphic plate  should  be  for  both  time  and  instantaneous  exposures. 
Take  the  case  of  the  discharge  passing  between  the  knobs  of  a  static 
machine  when  the  leyden  jars  that  accompany  the  machine  are  included. 
The  discharge  obviously  is  oscillatory  though  damped  rapidly.  Let  its 
general  character  be  represented  by  Fig.  I ,  in  which  the  ordinates  repre- 


Fig.  1. 

sent  successive  values  of  the  quantity  of  electricity  discharged  and  the 
abscissas  the  periodic  time  T.     This  period  is  given  by  the  relation 


_2  /  |~r^ 

~2lr/\IC      4L*' 


which,  as  R  diminishes,  approaches  the  value 

T  =  2w^LC. 
In  words,  the  curve  approaches  a  simple  sine  wave  with  no  damping. 


42  CHAS.  T.  KNIPP. 

If  such  an  electrical  pendulum  could  maintain  itself  in  the  case  of  our 
discharge  vessel,  the  kinetic  energy  would  remain  constant  and  there 
would  in  consequence  result  but  one  group  of  group  velocity  electrons. 
This  group  would  have  the  same  velocity  as  the  electrons  in  the  case  of  a 
continuous  discharge  corresponding  to  the  same  discharge  potential 
difference.  If  however  R  has  a  considerable  value,  as  is  the  case  that 
obtains  in  the  ordinary  operation  of  a  discharge  tube  by  a  static  machine 
or  induction  coil,  the  oscillations  are  damped  as  shown  in  Fig.  i.  The 
successive  quantities  discharged  through  the  tube  fall  off  rapidly,  and 
hence  the  energy  also  falls  off  rapidly.  This  results,  since  both  e  and  m 
remain  constant,  in  a  number  of  groups  of  electrons  (one  group  corre- 
sponding to  each  crest)  having  successively  smaller  and  smaller  velocities. 
Take  for  example  the  case  when  the  successive  ordinates,  both  positive 
and  negative,  are  proportional  to  3.0,  1.5,  i.o,  0.5,  0.32,  0.2,  0.12  centi- 
meters. If,  as  was  suggested,  the  velocities  of  the  resulting  electrons 
in  the  cathode  beam  are  proportional  to  these  ordinates  we  should  get 
by  equation  i,  for  the  electrostatic  displacement,  distances  proportional 
to  O.I  I,  i.o,  10,  25,  70.  And  similarly  by  equation  2,  for  the  magnetic 
displacement,  distances  proportional  to  0.33,  i.o,  3.3,  8.3.  These  dis- 
placements drawn  to  the  same  scale  are  set  down  in  Fig.  2.  Hence  the 


Fig.  2. 


number  of  beads  appearing  on  a  given  photographic  plate,  other  condi- 
tions remaining  constant,  is,  roughly,  inversely  as  the  damping  of  the 
oscillatory  discharge  which  gives  rise  to  them. 

The  degree  of  exhaustion  would  also  have  an  important  bearing  on  the 
appearance  of  the  beads.  For  a  given  set  of  conditions,  such  as  in  the 
example  above,  we  should  expect  that  the  higher  the  vacuum  the  greater 
the  velocity  of  the  group  electrons  and  hence  the  less  the  displacement. 
However,  if  the  vacuum  is  too  high  the  oscillations  after  the  first  one  may 
not  be  able  to  get  through  the  discharge  vessel,  and  for  very  high  vacua 
we  should  expect  but  the  one  group.  On  the  other  hand  if  the  vacuum  is 
low  the  velocity  of  the  successive  groups  will  be  low  and  hence  the  larger 
the  displacements.  The  latter  may  be  so  large  for  group  electrons  corre- 
sponding to  oscillations  after  the  first  that  these  groups  may  be  driven  off 
the  plate  by  the  deflecting  field.  For  low  vacua  the  absorption  will  be 
considerable  and  this  may  be  sufficient  to  prevent  the  slower  moving 
groups  from  reaching  the  plate,  or,  if  they  do  reach  it,  as  may  be  the  case 


CHARACTER   OF   CATHODE   RAY   LINE. 


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44  CHAS.  T.  KNIPP. 

when  the  deflecting  field  is  weak,  they  may  not  possess  enough  energy 
to  affect  the  photographic  film. 

DISCUSSION  OF  PHOTOGRAPHS. 

As  stated  at  the  outset  the  beaded  character  of  the  cathode  ray  line 
was  observed  accidentally  while  working  on  retrograde  rays.  The  shutter 
had  failed  to  work,  and  in  attempting  an  exposure  on  a  fresh  surface  the 
plate  was  turned  forward  while  the  discharge  was  passing.  The  plate 
when  developed  showed,  for  the  instantaneous  exposures,  a  marked 
beading.  Subsequently  the  beads  were  again  noticed,  especially  when 
one  or  the  other  of  the  deflecting  fields  was  zero.  The  beads  seemed  more 
pronounced  when  the  deflection  was  due  to  the  electrostatic  field  and 
hence  most  of  the  exposures  (except  a  few  at  the  beginning)  were  made 
with  H  equal  to  zero. 

Some  fifty  plates  were  exposed  with  especial  reference  to  this  beaded 
effect.  A  number  of  these  were  selected  as  representative  and  are  re- 
produced full  size  in  Plates  I.  and  II.  The  order  of  exposure  is  indicated 
on  each  photograph.  The  data  relative  to  these  photographs  are  collected 
in  Table  I.  It  may  be  well  to  state  that  if  looking  in  the  direction  of  the 
beam  of  cathode  rays,  the  plates,  in  exposing,  were  turned  counter  clock- 
wise. This  makes  the  order  on  the  reproduced  photographs  clockwise. 
The  exposures,  then,  begin  at  the  left  and  end  after  a  more  or  less  com- 
plete clockwise  revolution  near  the  beginning. 

The  photograph  reproduced  in  Fig.  3  was  the  first  to  show  beads.  The 
deflections  were  due  to  both  the  magnetic  and  electrostatic  fields  acting 
simultaneously.  In  the  first  half  the  direction  of  the  electrostatic  field 
was  such  as  to  drive  the  cathode  line  away  from  the  center.  This  field 
was  reversed  in  the  second  half.  The  instantaneous  exposures,  in  general, 
show  three  bright  spots  or  beads.  No  record  was  kept  of  the  vacuum; 
however,  it  was  not  high. 

The  reproduction  shown  in  Fig.  4  was  one  of  the  first  plates  exposed  in 
which  the  sole  object  was  to  get  the  beaded  effect.  During  the  interval 
the  diaphragms  used  in  Fig.  3  were  replaced  by  a  brass  tube  about  18 
mm.  long  by  .12  mm.  internal  diameter.  This  tube  gave  much  sharper 
definition.  The  vacuum  was  high  and  the  minimum  discharge  potential 
was  equivalent  to  a  2.5  cm.  spark  in  air.  In  this  and  the  photographs 
that  follow  the  electrostatic  field  only  was  employed.  The  photograph 
shows  a  series  of  instantaneous  exposures  with  X  (the  electrostatic  field) 
equal  to  zero,  a  time  exposure  of  10  or  15  seconds,  followed  by  another 
series  of  instantaneous  exposures  with  X  —  3,000  volts  per  centimeter, 
and  finally  a  time  exposure  of  about  one  second.  Many  of  the  instan- 


PHYSICAL  REVIEW,  VOL.  II.,  SECOND  SERIES 
July,  1913- 


PLATE  I. 
To  face  page  44. 


"<" 


^ 


'- 


Fig.  3. 


Fig.  4. 


rs, 


Fig.  5. 


Fig.  7. 


r 


PLATE  I. 

CHAS.  T.  KNIPP. 


Fig.  9. 


PHYSICAL  REVIEW,  VOL.  II.,  SECOND  SERIES 
July,  1913- 


PLATE  II. 

To  face  page  44. 


>\ 


I 


Fig.   10. 


Fig.   12. 


Fig.   13. 


Fig.  15. 


Fig.  14. 


Fig.  16. 


PLATE  II. 
CHAS.    T.    KNIPP. 


VOL.  II.- 

No.  i.    J 


CHARACTER   OF   CATHODE   RAY  LINE. 


45 


taneous  exposures  show  a  second  and  several  a  third  dot  in  the  direction 
towards  the  center  of  the  plate.  It  is  interesting  in  this  connection  to 
note  that  the  first  time  exposure  also  shows  the  retrograde  rays,  i.  e., 
carriers  atomic  in  size  and  charged  positively  and  hence  deflected,  in  this 
photograph,  away  from  the  center. 

The  conditions  for  Fig.  5  were  nearly  the  same  as  in  Fig.  4,  except  in 
the  second  half  of  the  revolution  a  capacity  of  two  leyden  jars  was 
included  as  shown  in  6,  Fig.  6.  The  connections  for  the  first  half  are 
shown  in  a  of  the  same  figure.  The  undeflected  spots  are  first  shown,  then 
the  plate  was  turned  through  an  arc  during  which  the  deflecting  field 
X  was  on,  after  which  X  was  reversed  for  a  time  and  then  again  reduced 
to  zero.  The  leyden  jars  were  now  included,  as  shown  in  Fig.  6,  b,  and 


Fig.  6. 

the  sequence  of  exposures  repeated.  Unfortunately  the  reproduction 
does  not  show  all  of  the  finer  markings  of  the  negative.  A  number 
of  the  exposures  on  the  negative  show  as  many  as  four  beads. 

In  the  succeeding  photographs  the  tube  was  replaced  by  the  objective 
containing  the  diaphragms.  The  three  photographs,  Figs.  7,  8,  9,  con- 
stitute a  series  of  instantaneous  exposures  in  which  all  the  conditions 
were  kept  constant  except  the  vacuum.  In  these  an  8  inch  Leeds  coil 
was  substituted  for  the  6  inch  Kohl  coil.  The  connections  were  those  of 
a,  Fig.  6.  The  method  of  exposing  each  plate  was  to  give  the  plate  a 
quarter  turn,  then  stop  for  a  few  seconds  before  proceeding  on  round. 
The  first  photograph,  Fig.  7,  shows  the  beads  in  a  striking  manner.  In 
the  second,  Fig.  8,  the  vacuum  was  some  higher  and  hence  the  displace- 
ment of  the  first  group  is  less.  The  exposures  on  this  plate  show  peculiar 
markings  in  the  neighborhood  of  the  undeflected  point  which  may  be  due 
to  ionization  or  secondary  effects.  These  markings  together  with  others 
that  appear  at  the  side  of  each  instantaneous  photograph  are  distinctly 
shown  in  the  third  photograph  of  this  series,  Fig.  9.  The  effect  of  an 
increasing  vacuum  is  to  cut  off  the  subsequent  groups.  Traces  of 
retrograde  rays  are  visible  in  nearly  all  of  the  time  exposures  on  these  three 
plates. 


46  CHAS.  T.  KNIPP.  [15SS 

In  the  next  three  photographs,  Figs.  10,  12,  and  13,  the  induction  coil 
was  replaced  by  a  Wehrsen  static  machine.  Smaller  values  of  X  were  also 
used.  In  Fig.  10  the  connections  were  made  as  sketched  in  Fig.  n. 
As  is  readily  seen  the  discharge  takes  place  at  B  without  preparation 
whenever  a  spark  passes  at  A.  The  volume  of  the  discharge  was  con- 
siderable. Most  every  instantaneous  exposure  on  the  negative  shows 


li    il 

fl 


Fig.  11. 

beads.  In  the  photograph  reproduced  in  Fig.  12  the  inductances  and 
leyden  jars  were  removed  and  connections  were  made  direct.  The 
vacuum  was  quite  high.  The  peculiar  markings  shown  in  Figs.  8  and 
9  again  appear.  These  markings  also  appear  very  distinctly  in  the  first 
half  of  Fig.  13.  It  would  thus  seem  that  they  are  not  dependent  upon 
the  source  of  the  discharge. 

To  get  still  further  evidence  on  the  possible  cause  of  the  beads  that 
so  persistently  appear  on  the  cathode  ray  line  I  followed  a  suggestion 
made  by  Mr.  O.  H.  Smith,  graduate  student  in  physics,  and  who  assisted 
me  in  making  a  number  of  the  exposures.  If  these  beads  are  due  to  the 
oscillatory  discharge  then  possibly  additional  evidence  may  be  had  by 
photographing  simultaneously  the  negative  crest.  This  could  be  done 
by  mounting  two  exactly  similar  canals  with  their  attending  equal 
electrostatic  fields  diametrically  opposite  in  the  apparatus,  so  that  either 
in  turn  may  serve  as  the  cathode.  The  plate  with  this  arrangement  to 
be  turned  but  a  half  revolution.  The  negative  crests  (corresponding  to 
the  troughs  in  Fig.  i)  should  appear  on  the  plate  as  instantaneous  photo- 
graphs diametrically  opposite  to  the  corresponding  photograph  for  the 
positive  crests.  Indeed,  this  point  may  be  tested  with  the  apparatus  as 
originally  constructed  by  giving  the  photographic  plate  a  half  turn  then 
interchange  the  connections  after  which  the  turn  is  completed.  A  plate 
thus  exposed  should  show  negative  crests,  obviously  not  simultaneously 
with  the  positive  crests,  but  negative  crests  due  to  oscillations  accom- 
panying a  series  of  later  discharges,  and,  so  far  as  comparing  the  position 
of  the  negative  crest  with  the  positive  trough  is  concerned,  should 
answer  equally  well. 


VOL.  II. 
No 


5",.  ' ]  CHARACTER   OF   CATHODE   RAY   LINE.  47 


The  second  half  of  Fig.  13  was  taken  under  the  above  conditions.  It 
shows  that  cathode  rays  do  proceed  from  the  anode.  Their  presence  and 
position  may  be  accounted  for  by  the  negative  crests  of  the  damped 
oscillatory  discharge.  In  this  photograph  they  did  not,  however,  accom- 
pany each  discharge,  but  only  about  every  fourth  one,  though  careful 
measurements  show  that  the  groups  that  are  recorded  correspond  in 
general  to  the  troughs  in  the  first  half. 

In  Fig.  14  the  static  machine  was  replaced  by  the  8  inch  Leeds  induction 
coil,  the  vacuum  was  rather  low,  and  X  was  made  1, 800  volts  (see  Table 
I.).  On  this  plate  the  negative  crests  appeared  in  great  numbers  due  in 
part  to  the  plate  being  turned  more  slowly  in  the  second  half.  For  the 
most  part  their  positions  correspond  to  a  trough  in  the  first  half,  as  may 
be  seen  by  the  arc  drawn  on  the  photograph.  It  seems  strange,  however, 
that  this  photograph  shows  no  negative  crests  corresponding  to  the  fiist 
trough.  In  the  next,  Fig.  15,  X  was  made  3,000,  otherwise  the  conditions 
were  the  same  as  in  the  preceding  photograph.  In  this  negative  crests 
appear  in  the  second  half  corresponding  to  two  troughs  in  the  first  half. 

In  the  last  photograph  exposed,  Fig.  16,  the  tube  was  again  inserted. 
The  vacuum  though  not  recorded  was  high.  In  turning  the  plate  it  was 
halted  twice,  possibly  for  one  or  two  seconds,  in  each'  half  turn.  Again 
the  points  appearing  in  the  second  half  correspond  to  carriers  having  a 
lower  velocity  than  in  the  first  half.  In  comparison  with  Figs.  4  and  5 
it  is  evident  that  the  vacuum  was  too  high,  since  apparently  only  the  first 
positive  and  first  negative  group  electrons  were  formed. 

CONCLUSION. 

It  appears  from  the  photographs  reproduced  in  this  paper  that  in  most 
cases  the  beaded  effect  of  the  cathode  ray  line  may  be  accounted  for  by 
the  oscillatory  character  of  the  electric  discharge.  However  a  number  of 
the  photographs  show  beads  whose  spacing  along  the  cathode  line  is  not  in 
agreement  with  that  that  should  follow  for  damped  oscillations.  These 
may  be  due  to  ionization  or  secondary  effects,  or  possibly  due  to  group 
velocity  electrons  given  off  by  the  cathode.  The  position  of  the  cathode 
seems  to  have  but  little  or  no  effect  upon  the  general  character  of  the 
beads. 

The  strongest,  and  in  some  respects  the  most  convincing  evidence 
pointing  to  the  oscillatory  discharge  as  the  origin  of  the  beads  is  furnished 
by  the  photographs  showing  the  negative  crests.  These  crests  in  most 
every  instance  correspond  to  the  troughs  in  the  beaded  line  as  shown  in 
Figs.  13,  14,  15,  and  16. 


48  CHAS.  T.  KNIPP.  [1S?ESD 

Admitting  that  the  evidence  submitted  is  sufficient  to  show  that  an 
oscillatory  electric  discharge  under  proper  conditions  (conditions  which 
were  met  in  a  number  of  the  foregoing  photographs)  results  in  a  beaded 
cathode  ray  line,  it  seems  that  we  have  here  a  possible  explanation  of  the 
beading  of  J.  J.Thomson's  molecular  lines.1  This  conclusion,  it  seems 
to  me,  follows  naturally  because  of  the  intimate  relation  that  exists  be- 
tween the  cathode  rays  and  the  positive  rays  which  form  the  molecular 
line. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
March,  1913. 

1  Philosophical  Magazine,  August,  1912,  p.  237. 


ON  THE  PRESENT  THEORY  OF  MAGNETISM  AND  THE 
PERIODIC  SYSTEM  OF  CHEMICAL  ELEMENTS 

JACOB  KUNZ 

ABSTRACT 

The  Eighth  International  Congress  of  Applied  Chemistry,.  V.  XXII, 

p.  187. 


The  paper  discusses  the  following  topics : 

1.  Fundamental  assumptions. 

2.  Experimental  facts,  diamagnetism,  additive  and  non-additive  proper- 
ties. 

3.  The  periodic  system  of  the  elements  and  their  magnetic  properties. 

4.  Thermomagnetism. 

5.  The  magneton  of  Weiss  and  the  degrees  of  freedom. 

It  is  shown  that  the  elementary  charge  of  electricity  can  be  deter- 
mined by  the  magnetic  properties,  the  average  of  six  values  being 
e=  1.53.  io-20. 


Reprinted  from  the  ASTROPHYSICAL  JOURNAL,  Vol.  XXXVIII,  No.  2,  Sept.,  1913 


THE  USE  OF  THE  PHOTO-ELECTRIC  CELL  IN  STELLAR 

PHOTOMETRY 

PRELIMINARY  NOTE 
BY  W.  F.  SCHULZ 

The  great  sensitiveness  of  the  photo-electric  cell  has  been  shown 
experimentally  by  Elster  and  Geitel,1  by  Nichols  and  Merritt,2  and 
by  J.  G.  Kemp.3  From  the  results  of  these  investigations  it  seemed 
that  such  a  cell  might  be  used  to  measure  the  light  from  fixed  stars, 
and  its  variation.  The  following  is  an  account  of  some  successful 
preliminary  experiments  in  an  attempt  to  make  such  measurements. 


Diagram  of  apparatus 

Several  cells  of  the  form  shown  in  the  accompanying  diagram 
were  prepared  in  the  following  way.  The  anode  was  a  platinum 
wire  about  o .  5  mm  in  diameter,  bent  into  a  rectangular  loop  about 
iX  ij  cm  on  the  side,  the  terminal  passing  through  a  glass  sleeve  3 
or  4  cm  long.  On  the  wall  of  the  tube  facing  the  plane  of  this  loop 
was  a  layer  of  potassium  which  formed  the  cathode.  In  order  to 
have  good  contact  at  the  cathode  a  layer  of  silver  was  deposited  on 
and  around  the  platinum  terminal  on  the  inside  of  the  bulb.  The 


1  Physikalische  Zeitschrift,  13,  468,  1912. 

2  Physical  Review,  34,  476,  1912. 

187 


Ibid.  (2),  i,  274,  1913. 


i88  W.  F.  SCHULZ 

bulb  proper  was  about  5  cm  in  diameter.  Potassium  was  distilled 
from  a  similar  bulb  into  a  second  one,  then  poured  into  a  pocket  in 
the  tube  just  outside  of  the  bulb  of  the  photo-electric  cell  and 
finally  distilled  upon  the  silver  surface  surrounding  the  cathode 
terminal. 

A  little  hydrogen  gas  was  then  introduced  by  heating  a  strip  of 
palladium  contained  in  a  side  tube.  A  potential-difference  of  560 
volts  D.C.  was  applied  to  the  electrodes  Pt  and  P2,  Pz  being  negative, 
with  a  lamp  resistance  of  3000  ohms  in  series  with  the  cell.  When 
the  circuit  was  closed  for  a  few  seconds  the  bright  metallic  colors  of 
the  hydrogen  compound  appeared  at  once  on  the  potassium.  There 
was  a  uniform  soft  glow  over  the  entire  surface  of  the  metal,  the  rest 
of  the  bulb  being  non-luminous.  It  was  found  necessary  to  use  a 
rather  high  potential-difference  with  a  resistance.  When  a  potential- 
difference  of  300  volts  with  little  or  no  resistance  was  applied,  the 
discharge  took  the  form  of  an  arc  rather  than  that  of  a  glow,  and  the 
current  rose  rapidly,  in  one  case  even  melting  the  electrode. 

The  circuit  was  broken  when  the  surface  of  the  potassium  had 
assumed  a  brilliant  violet-blue  color  and  the  hydrogen  was  carefully 
pumped  out  and  was  replaced  by  a  small  quantity  of  helium.  All 
traces  of  oxygen  were  removed  from  the  helium  by  passing  it 
through  a  tube  in  which  potassium  was  evaporated,  before  intro- 
ducing it  into  the  cell.  The  photo-electric  cell  was  next  connected 
in  series  with  a  sensitive  galvanometer  and  the  lamp  resistance,  and 
a  potential-difference  of  300  volts  was  applied.  The  light  from  a 
small  gas  flame  was  allowed  to  fall  on  the  metal  of  the  cell,  and  the 
pressure  in  the  latter  was  varied  by  small  steps  until  the  galva- 
nometer deflection  was  a  maximum.  The- tube  was  then  sealed  off 
and  proved  to  be  constant  for  a  period  of  several  months. 

For  measuring  very  small  intensities  of  light  two  different 
methods  were  used.  In  the  colder  winter  months,  especially  in  the 
open  observatory,  the  temperature  of  the  cell  was  so  low  that  the 
natural  leak  through  the  dark  cell  was  negligible,  and  the  photo- 
electric current  was  measured  directly  by  the  rate  of  deflection  of 
a  quadrant  electrometer.  Toward  the  spring,  however,  when  the 
temperature  rose,  the  natural  leak  through  the  cell  increased  rapidly 


PHOTO-ELECTRIC  CELL  IN  STELLAR  PHOTOMETRY       189 

with  the  temperature,  and  it  was  found  necessary  to  compensate 
this  current  by  means  of  an  independent  circuit  as  shown  in  the 
diagram.  The  anode  of  the  cell  was  connected  to  a  storage  battery 
of  1 60  cells,  the  negative  terminal  of  which  was  earthed.  The 
cathode  was  earthed  through  a  high  resistance  Rt  and  connected 
through  a  discharge  key  to  one  pair  of  quadrants  of  a  Dolezalek 
electrometer.  In  the  compensating  circuit  a  battery  of  3  cells  sent 
current  through  a  variable  resistance  R2R3  of  20,000  ohms,  and  the 
negative  terminal  was  earthed.  The  other  pair  of  quadrants  was 
connected  to  R2R3  by  means  of  a  traveling  plug.  By  this  arrange- 
ment the  "dark  current''  could  be  completely  neutralized.  Vr  was 
varied  from  150  to  320  volts.  This  was  not  quite  the  upper  limit  at 
which  the  cell  could  be  used,  but  350  volts  was  too  large,  and  the 
photo-electric  current  reached  a  value  beyond  that  of  saturation. 
R!  was  a  very  high  resistance  of  xylol  with  just  a  trace  of  pure 
alcohol.  The  sensitiveness  of  the  electrometer  was  such  that  a 
potential  difference  of  20  volts  on  the  needle  and  i .  4  volts  between 
the  quadrants  produced  a  deflection  of  120  mm  at  a  scale-distance  of 
2  meters.  The  deflections  were  very  steady.  The  cell  was  tested 
by  the  light  from  a  small  incandescent  lamp,  which  was  cut  down  by 
passing  it  through  two  large  crossed  Nicol  prisms.  The  cell  was 
mounted  in  a  light-tight  box,  carefully  blackened  inside,  and  closed 
by  means  of  a  shutter.  A  long  closed  tube  was  screwed  into  the 
opening  of  the  box,  and  the  lamp  placed  in  this  at  1.5  meter 
distance  from  the  cell.  The  Nicols  were  inserted  between  lamp  and 
cell,  with  a  device  for  measuring  and  varying  the  angle  between 
them.  The  candle-power  of  the  lamp  measured  on  a  two-meter 
photometer  with  Lummer-Brodhun  screen  was  approximately 
0.003  at  6  volts.  The  deflections  of  the  electrometer  were  easily 
read  even  when  the  planes  of  polarization  made  an  angle  of  85°  with 
each  other.  The  intensity  of  the  light  which  passed  through  an 
opening  of  i  sq.  cm  area  at  the  cell  was  therefore  o.  003  X  cos2 
&5/1  •  52 =0.000010  candle  meters. 

It  has  been  shown  by  Angstrom  that  the  energy  flowing  from  an 
amyl  acetate  lamp  is  approximately  10— 8  gram  calories  per  square 
cm  at  a  distance  of  i  meter.  Assuming  the  Hefner  unit  and  the 


190  W.  F.  SCHULZ 

candle-power  to  be  equal  and  the  distribution  of  energy  to  be  the 
same  in  both  lamps,  we  find  that  the  quantity  of  energy  incident  on 
the  cell  is  approximately  0.000010X10— 8  gram  calories  or  4.  igX 
10— 6  ergs.  This  produces  a  deflection  of  the  electrometer  which  is 
easily  read.  So  far  the  light  from  two  stars  has  been  measured  by 
means  of  this  cell;  in  December  1912,  that  of  Capella  and  in  April 
1913,  that  of  Arcturus.  The  cell  in  its  light-tight  box  was  mounted 
on  the  i2-inch  equatorial  at  the  observatory  of  the  University  of 
Illinois,  and  placed  in  such  a  position  beyond  the  focal  plane  of  the 
objective  that  the  circle  of  illumination  on  the  sensitive  surface  of 
the  cell  had  an  area  of  about  i  sq.  cm. 

On  the  cold  December  nights  the  natural  leak  through  the  cell 
was  almost  zero,  and  the  photo-electric  current  was  measured  by  the 
rate  of  the  electrometer  deflection.  With  40  volts  on  the  needle 
and  1 60  volts  on  the  cell,  the  rate  of  deflection  at  a  scale-distance  of 
2  meters  was  20  mm  in  30  seconds.  With  200  volts  on  the  cell,  the 
rate  was  18  mm  in  20  seconds.  These  deflections  were  repeated 
without  difficulty. 

In  April  1913,  another  set  of  readings  was  taken  with  the  light 
from  Arcturus.  This  time  the  dark  current  had  to  be  compensated. 
With  60  volts  on  the  needle  and  250  on  the  cell,  the  deflection  due  to 
the  photo-electric  current  alone  was  22  mm.  This  was  reduced  to 
zero  each  time  by  varying  the  resistance  R3.  With  60  volts  on  the 
needle  and  300  on  the  cell,  the  deflection  when  the  cell  was  exposed 
to  the  light  of  Arcturus  was  48  mm;  with  60  volts  on  the  needle  and 
325  on  the  cell  the  deflection  was  190  mm;  and  with  80  volts  on  the 
needle  and  325  on  the  cell  the  deflection  was  248  mm.  The  sensi- 
tiveness of  both  cell  and  electrometer  can  be  increased. 

These  measurements  seem  to  show  that  it  is  possible  to  use  the 
photo-electric  cell  for  astrophysical  investigations.  The  present 
research  is  being  continued  along  various  lines.  It  is  planned  to 
compare  the  sensitiveness  of  the  photo-electric  cell  with  that  of  the 
selenium  cell,  and  to  study  the  influence  of  temperature  upon  the 
"dark  current,"  the  effect  of  the  wave-length  of  the  incident  light 
upon  the  lower  limit  of  sensitiveness,  and  the  use  of  various  alkali 
metals  for  the  sensitive  layer. 


PHOTO-ELECTRIC  CELL  IN  STELLAR  PHOTOMETRY       191 

These  measurements  were  made  at  the  suggestion  of  my  friend 
Dr.  Jakob  Kunz,  to  whom  I  am  deeply  indebted  for  the  benefit  of 
his  invaluable  experience  in  making  the  cells  and  for  assistance  in 
conducting  the  experiments. 

UNIVERSITY  OF  ILLINOIS 
May  19,  1913 


(Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  II..  No.  3,  September,  1913.] 


THERMAL    AND    ELECTRICAL    CONDUCTIVITIES    OF   THE 

ALKALI    METALS. 


O 


BY  J.  W.  HORNBECK. 

I.   INTRODUCTION. 

NE  of  the  first  successes  of  the  modern  electron  theory  consisted  in 
its  very  simple  explanation  of  the  constant  ratio  of  the  thermal 
and  electrical  conductivities  for  the  metallic  elements.  However,  a 
closer  study  of  the  conduction  of  heat  and  electricity  through  metals,  of 
their  thermo-electric  and  magnetic  properties,  showed  that  the  simple 
theory,  which  considered  the  electrons  to  move  freely  through  the  metal, 
was  unable  to  explain  the  manifold  and  complicated  phenomena  in  a 
satisfactory  way. 

It  was  first  assumed,  in  the  theories  of  Riecke,  Drude,  J.  J.  Thomson 
and  H.  A.  Lorentz,  that  the  electrons  are  free  and  share  the  heat  motion 
of  the  atoms;  but  this  assumption  leads  to  a  number  of  contradictions. 
When  one  determines  TV,  the  number  of  free  electrons  per  cubic  centi- 
meter, by  the  method  of  the  conductivities  for  heat  and  electricity  for 
the  different  metals,  values  are  found  which  differ  greatly1  from  those 
derived  from  the  Peltier  effect.  Moreover,  the  experiments  of  Rubens 
and  Hagen  show  that  the  electrical  conductivity  of  metals  for  alternating 
currents  of  very  high  frequency  remains  practically  the  same  as  for  steady 
forces,  and  the  values  of  N  which  follow  from  these  data  are  impossible1 
in  view  of  the  known  values  of  the  specific  heat.  Furthermore,  Lees2 
measured  the  thermal  and  electrical  conductivities  of  a  number  of  metals 
down  to  the  temperature  of  liquid  air  and  found  an  increasing  deviation 
from  the  law 

x  _  4  c?  „ 

;~5?  ^ 

A  change  in  structure  has  a  large  effect  on  the  thermal  and  electrical 
conductivities.  For  instance  it  has  been  found  recently3  that  the  re- 
sistance of  mercury  at  4.2°  absolute  drops  suddenly  from  o.n  to  zero. 
Small  impurities  have  large  effects.  Metals  and  alloys  often  behave  in 
opposite  ways.  For  example,  the  heat  conductivity  of  the  metals  de- 

1  J.  J.  Thomson,  Corpuscular  Theory  of  Matter,  pp.  76,  84. 

2  C.  H.  Lees,  Phil.  Tran.,  Royal  Soc.,  Vol.  208,  p.  381,  1908. 

8  H.  Kamerlingh  Onnes,  Com.  Phys.  Lab.  of  Univ.  of  Leiden,  No.  124,  p.  23. 


218  J.  W.  HORN  BECK. 

creases  slightly  with  increasing  temperature,  while  for  the  alloys  it  in- 
increases  with  the  temperature.  Moreover,  the  ratio  \/<rT  increases 
slightly  between  —  180°  C.  and  +  20°  C.  for  the  metals,  and  decreases 
considerably  for  the  alloys. 

These  facts  cannot  be  explained  by  the  present  theories  even  when  it 
is  assumed,  as  Lorentz  and  Richardson1  have  done,  that  the  distribution 
of  the  velocities  of  the  electrons  is  that  which  corresponds  to  Maxwell's 
expression. 

The  strongest  evidence  against  this  conception  of  the  electric  current 
consists  in  the  fact,  shown  by  Nernst,  that  the  specific  heat  of  metals 
approaches  zero  as  the  temperature  approaches  the  absolute  zero.  If 
the  current  were  due  to  the  motion  of  free  electrons  which  are  in  tempera- 
ture equilibrium  with  the  metal,  then  the  specific  heat  would  be  due 
mainly  to  the  free  electrons  and  would  therefore,  as  in  a  gas,  change  very 
little  with  decreasing  temperature.  The  question  arises  as  to  whether 
the  electrons  carrying  the  current  take  part  in  the  specific  heat. 

Several  modifications  of  the  original  theory  have  been  proposed,  but 
none  of  them  gives  an  adequate  quantitative  explanation  of  all  the 
phenomena.  The  various  theories  agree  only  in  the  fundamental  as- 
sumption that  the  current  is  carried  by  electrons.  This  is  in  harmony 
with  the  general  facts  that  the  good  conductors  are  metals,  positive 
elements,  ready  to  part  with  a  negative  electron;  that  the  metals  when 
struck  by  ultra-violet  light  or  Roentgen  rays,  or  when  heated  to  a 
certain  temperature,  emit  electrons;  and  that  the  current  in  the  metals 
shows  the  Hall  effect. 

The  decrease  of  the  specific  heat  with  decreasing  temperature  is  at 
least  qualitatively  accounted  for  by  Planck's  theory  of  radiation.  It  is 
possible  that  the  electrons  have  at  low  temperature  no  part  in  the  specific 
heat  of  the  metals,  so  that  the  specific  heat  is  entirely  due  to  the  motion 
of  the  atoms  or  to  their  elementary  oscillators.  According  to  this  con- 
ception there  are  no  free  electrons  at  all,  at  least  at  low  temperatures, 
and  the  electrons  escape  only  when  they  have  acquired  a  sufficient 
amount  of  kinetic  energy  to  overcome  the  attraction  of  the  positive 
"rest-atom."  Then  there  should  be  a  definite  relation  between  the 
energy  of  the  electron  and  the  energy  of  the  atom. 

We  shall  assume  that  the  electrons  part  with  the  atom  when  their 
kinetic  energy  is  proportional  to  the  energy  E  of  the  atom.  Moreover, 
for  the  energy  of  the  atom,  or  the  oscillator  in  the  atom,  we  shall  assume 
the  expression  given  by  Planck2 

1  Planck,  Acht  Vorlesungen  iiber  Theoretische  Physik. 

2  O.  W.  Richardson,  Trans.  Am.  Chem.  Soc.,  Vol.  XXL,  1912. 


No's"']  CONDUCTIVITIES  OF  ALKALI   METALS.  2ig 


or,  according  to  the  modified  theory, 


, 

r  ~  • 


Then  the  kinetic  energy  of  the  electron  is  given  by 

hn 

—  7  ~J^,        > 


where  7  is  some  constant,  and  from  this  equation  we  know  v  as  a  function 
of  T.  The  constant  term  hn/2  has  no  effect  in  the  present  application 
of  the  Planck  theory.  If  /  is  the  mean  free  path  and  t  the  time  during 
which  the  electron  moves  from  one  atom  to  the  other,  then 

t 

v  =  -. 

The  force  acting  on  the  electron  in  the  field  E'  is  E'e,  and  the  acceleration 

E'e 

a  =  —  . 
m 

The  mean  time  during  which  this  force  acts  is  t/2  seconds  and  hence  the 
field  superposes  a  velocity 

at      E'el 

u  —  —  —  -  . 

2,       2mv 

The  number  of  electrons  passing  through  unit  cross-section  per  unit 
time  is 

NE'el 


Nu  =  , 

2mv 


and  the  current  density 

.       A7 
i  =  Nue 

Whence 


Nlve2  _     Nlve*.    \ 
Ei   :  hn    ' 


For  the  quantity  of  heat  energy  passing  through  unit  area  per  unit  time, 
we  have 


22O  J.  W.  HORNBECK. 

i         SEj.      i  -..dEidT        dT 

H  =  -  Nvl  -T—  =  -  Nvl  -j=  -3-  =  X  -j  . 
3          d#       3         dr  d#          d# 

And 


Hence 

X       4 


,  . 

(3) 


Substituting  in  (3)  the  values  of  EI  and  dEi/dT,  we  have 


hn 

X        4  72/&3«3    I          ekT 
oT  ~  z     ezk     T 


If  hn/kT  is  small,  we  can  expand  the  exponential  functions  and  equa- 
tion (4)  for  the  higher  temperatures  assumes  the  form 

X   _4    2) 

~vT  ~  3  T  " 

As  T  increases,  according  to  equation  (5),  the  values  of  \/<rT  should 
approach  a  constant  value  and  this  agrees  with  the  facts.  Moreover » 
when  the  values  of  X/oT  are  plotted  against  T  in  equation  (4),  the  curve 
is  found  to  be  of  the  same  form  as  the  experimental  curves  which  Lees 
obtained  for  the  pure  metals  at  low  temperatures.  Thus  we  have  a 
formula  which  explains  the  behavior  of  \jaT  for  pure  metals  and  which 
also  leads  approximately  to  the  right  expression  for  the  variation  of  the 
specific  heat  with  the  temperature.  It  agrees  with  Einstein's  formula 
for  specific  heat;  in  fact,  both  formulae  rest  upon  Planck's  expression 
forE. 

It  is  not  claimed  that  this  theory  is  complete.  It  is  merely  suggested 
as  a  possible  step  in  the  right  direction  because  it  removes  two  important 
difficulties  of  the  electron  theory  without  introducing  new  contradictions. 
The  phenomena  of  metallic  conduction  are  so  complicated  that  they 
cannot  be  explained  by  one  simple  group  of  assumptions.  So  far  we  have 
considered  only  the  heat  conductivity  due  to  the  electrons.  The  atoms 
themselves  undoubtedly  transfer  a  part  of  the  heat  motion  as  is  shown 
by  the  fact  that  non-conductors  of  electricity  have  finite  values  of  X 
while  o-  is  equal  to  zero.  Moreover,  there  are  good  reasons  for  believing 
/,  the  mean  free  path,  is  a  function  of  the  temperature.  This  would  fol- 
low from  Richard's  theory  in  regard  to  the  variation  of  the  radius  of  the 
atom.  It  should  be  pointed  out  that  if  we  take  the  two  most  simple 
formulas 


CONDUCTIVITIES  OF  ALKALI  METALS.  221 


X  =  -  Nlva, 
o 

Nie* 


and  assume  y<#ntf  =  aT  and  also  /  =  const  /Vr,  it  follows  that  X  be- 
comes independent  of  the  temperature,  while  a-  is  inversely  proportional 
to  the  absolute  temperature.  This  agrees  fairly  well  with  experimental 
facts  over  a  considerable  range  of  temperature.  That  the  mean  free 
path  has  something  to  do  with  the  conductivity  is  also  shown  by  the  Hall 
effect.  H.  Kamerlingh  Onnes  has  found  that  the  constant  of  the  Hall 
effect  for  gold,  silver  and  mercury,  increases  considerably  near  the  tem- 
perature of  liquid  hydrogen. 

Finally,  the  electric  field  may  act  on  the  atoms  in  a  metal,  tending  to 
bring  about  a  certain  polarization  which  will  have  an  effect  on  the  con- 
ductivity for  electricity  and  heat.  If  this  were  the  case,  we  should 
expect  the  use  of  temperature  baths  to  lead  to  a  value  of  X  different  from 
that  obtained  by  electric  heating. 

It  was  the  purpose  of  the  present  investigation  to  attempt  to  bring 
further  evidence  in  favor  of  one  of  the  different  theories.  The  alkali 
metals  were  thought  to  be  particularly  suited  to  this  purpose  because 
they  have  properties  quite  different  from  those  of  the  other  metals. 
Alkali  metals  have  a  higher  temperature  coefficient  of  resistance  than 
the  other  metals.  The  atomic  heat  and  atomic  volume  are  greater  and  the 
index  of  refraction  smaller  than  for  the  ordinary  metals.  In  their  photo- 
electric properties  they  differ  considerably  from  the  other  elements. 
All  these  properties  indicate  that  the  alkali  metals  are  rich  in  electrons 
and  that  even  the  positive  "rest-atoms"  have  considerable  mobility. 

So  far  as  known,  the  heat  conductivity  of  the  alkali  metals  has  hitherto 
not  been  measured.  This  is  a  constant  of  sufficient  importance  to  make 
its  determination  worth  while.  Northrup1  has  determined  the  electrical 
conductivity  of  the  ajkali  metals  by  a  very  good  method  and  claims  an 
accuracy  of  one  half  of  one  per  cent.  His  results,  however,  do  not  agree 
well  with  those  of  former  observers2  and  it  was  therefore  considered 
important  to  check  his  work  by  an  entirely  different  method. 

II.   THEORY  OF  THE  METHOD. 
The  original  Kohlrausch3  method,  which  was  perfected  by  Jaeger  and 

1  E.  F.  Northrup,  Trans.  Am.  Electro-Chem.  Soc.,  Vol.  XX.,  1911,  p.  185. 

2  Mattheisen,  Phil.  Mag.  (4),  12,  199,  1856;  13,  81,  1857.     Bernini,  Phys.  Zeit.,  5,  241,  1904. 

3  F.  Kohlrausch,  Gott.  Nachr.,  S.  83,  1874;  Pogg.  Ann.,  156,  S.  616,  1875;  Ann.  der  Phys., 
(4)  I..  145,  1900. 


r  r~Yf 
M,I  _  ^ 

/t     X.+AT-  <L* 


222  J.  W.  HORN  BECK. 

Diesselhorst,1  was  used.  It  is  both  simple  and  reliable  and  it  has  the 
distinct  advantage  of  giving  the  ratio  of  the  heat  and  electrical  conductivi- 
ties directly.  This  method  consists,  briefly,  in  sending  a  steady  electric 

current  through  a  cylindrical  rod  of 
the  metal  to  be  investigated  and 
measuring  the  temperature  and  po- 
tential difference  at  three  equidistant 
Fig.  1. 

points  along  the  axis  of  the  rod,  while 

the  temperatures  of  the  ends  of  the  rod  and  of  the  surrounding  jacket  are 
held  constant.  For  the  convenience  of  the  reader  the  theory  of  the 
method,  so  far  as  it  has  any  application  to  this  investigation,  will  be 
given  here  in  a  simplified  form. 

Referring  to  Fig.  I ,  let  u  and  v  represent  the  temperature  and  potential 
of  any  cross-section  of  the  rod ;  and  let 

a  =  area  of  cross-section, 
<r  —  electrical  conductivity, 
X  =  thermal  conductivity. 

Let  us  assume  that  the  Thomson  effect  is  negligible  and  that  X  and  cr, 
for  the  small  temperature  interval  considered,  are  constant.  Then  the 
current  flowing  through  the  rod  is  given  by 

_<fo\ 
dxj* 

And  the  number  of  calories  of  heat  developed  in  the  elementary  volume 
per  unit  time  is 

dO  =  -    —    - 
<r     a     J1 

where  J  represents  Joule's  equivalent, 


The  quantity  of  heat  flowing  into  the  elementary  volume  per  unit 
time  is 


dQ,  =  i-  — 

and  the  quantity  flowing  out  is,  likewise,  equal  to 

du  d2u 

dQz  —  — r~  X&  — r~o  Xflkwc. 
dx  dx2 

1  Jaeger  und  Diesselhorst,  Wiss.  Abh.  der  Phys.  Tech.  Reich.,  3,  269,  1890;  Sitz.  Ber.  Der 
Berlin  Ak.  d.w.,  38,  719,  1899. 


CONDUCTIVITIES   OF  ALKALI   METALS.  22$ 

For  the  stationary  state 

dQ  +  dQi  —  dQ2  —  o.  (l) 

Substituting  in  this  equation,  we  have 

T      ^w     _=  Q 

Now  the  isothermal  surfaces  are  also  equipotential  surfaces,  if  we 
assume  that  the  temperature  is  constant  for  all  points  of  the  same  cross- 
section,  and  the  temperature  depends  upon  the  potential  only.  Then 


du      du  dv 
dx      dv  dx' 
And 

d?u  _  dzu  fdv  y^  du  d*v 
dx2      dv2  \dx 
But 


)' 


d2u      d2u  f  dv  \2 
dxz      dv2  \dxj  ' 


Substituting  this  value  in  equation  (2),  we  have 

d?udv 


dx 
Or 

d2u  _         <r 

~d^=    ~7x*  (3) 

Integrating  this  equation,  we  have 

The  integration  constants,  A  and  B,  are  readily  evaluated  by  imposing 
the  condition 

and  the  equation  can  be  reduced  to  the  form 

X  _  I     £     (PI  -  fla)2  ,  , 

<7  ~  8  "  / '    «2  -  «'   * 

where  u%  is  the  temperature  of  the  middle  of  the  rod,  and  u'  is  the  tem- 
perature of  either  of  the  two  sections  equally  distant  from  the  middle. 


224  J-  W.  HORNBECK.  [§ER?ESD 

Equation  (5)  would  be  true  if  no  heat  were  lost  through  the  lateral 
surface  of  the  rod.  This  condition,  however,  cannot  be  realized  experi- 
mentally and  so  it  is  necessary  to  apply  a  correction. 

Let  us  change  (5)  slightly  by  expressing  X  in  watt-seconds,  instead  of 
calories,  and  put 

V  = 


U  =   Ui  —  U'   =   U2  —   %(Ui  +  «3). 

Then  we  have 


In  this  equation,  then,  U  stands  for  the  value  of  the  temperature  differ- 
ence, supposing  that  the  surface  of  the  rod  were  covered  with  a  perfect 
heat  insulator. 

Now  let  A  represent  the  observed  value  of  the  temperature  interval 
uz  ~~  %(ui  +  ^3)  ;  let  UQ  represent  the  temperature  of  the  surrounding 
jacket;  and  let 

N  =   UQ  -  U2  +  JA. 

Then,  as  Jaeger  and  Diesselhorst  have  shown,1 

U  =  A  -  eN,  (7) 

where  e  is  a  correction  factor  depending  on  the  conductivity  of  the 
packing,  the  conductivity  of  the  metal,  and  the  dimensions  of  the  rod 
experimented  upon;  and  its  value  can  be  determined  by  experiment. 
In  the  present  work  with  the  alkali  metals,  the  values  of  X/<r  were 
computed  by  means  of  equations  (6)  and  (7). 


for  the  case  where  no  heating  current  is  used.    The  method  of  obtaining 
this  correction  factor  will  be  made  clear  in  a  later  chapter. 

III.    APPARATUS. 

End  Baths.  —  The  apparatus  for  controlling  temperatures  was  con- 
structed in  the  department  shop.  It  was  modeled  after  that  of  Jaeger 
and  Diesselhorst,  but  certain  modifications  were  necessary  in  order  to 
protect  the  glass  vacuum  tubes  which  contained  the  alkali  metals.  The 
end  baths  were  provided  each  with  a  flat  brass  lid  and  a  rotary  stirrer, 
as  shown  in  Fig.  2,  which  was  driven  by  a  small  motor.  Fig.  3  indicates 
the  method  used  to  attach  the  glass  tubes  to  the  end  baths.  In  a  way 

1  Wiss.  Abh.  der  Phys.  Tech.  Reich.,  3,  285,  1900. 


VOL.  II.-J 
No.  3.   J 


CONDUCTIVITIES  OF  ALKALI   METALS. 


225 


to  be  described  in  detail  later,  the  metal  to  be  studied  was  poured  into 
glass  tubes  one  or  two  centimeters  in  diameter  and  30  cm.  long.  The 
ends  of  the  tube  were  closed  by  copper  discs,  2  mm.  thick  and  5^/2  cm. 
in  diameter.  By  means  of  suitable  brass  rings,  each  provided  with  six 


Fig.  2. 

screws,  the  end-discs  were  attached  to  annular  diaphragms  which,  in 
turn,  were  mounted  against  the  end  baths  in  a  similar  way  so  that  the 
alkali  metal  and  the  water  were  separated  only  by  the  thin  discs  of  copper. 
The  soft-rubber  diaphragms  served  as  a  protection  for  the  glass  tubes 
against  mechanical  strains. 

The  heating-current  terminals  were  introduced  beneath  the  heads 
of  three  of  the  screws  symmetrically  placed  with  respect  to  the  center 
of  the  discs. 

Brass  Jacket. — The  temperature  of  the  atmosphere  of  the  tubes 
was  controlled  by  pumping  water  from  a  reservoir  through  a  cylindrical 


UD 


Fig.  3. 


Fig.  4. 


brass  jacket  by  means  of  a  small  turbine.  This  jacket  was  made  in  two 
independent  parts  which  were  connected  at  A  and  B  (Fig.  4),  and  simi- 
larly on  the  opposite  side,  by  short  rubber  tubes,  thus  making  it  necessary 
for  the  water  to  flow  the  entire  length  of  both  semi-cylinders  before 
leaving  the  jacket.  The  wires  of  the  thermo-couples  were  introduced 
between  the  two  parts  of  the  jacket  and  were  insulated  from  the  brass 
by  thin  strips  of  mica. 

The  temperature,  UQ,  of  the  jacket  was  measured  by  two  Beckmann 
thermometers,  mounted  deep  within  vertical  glass  tubes  through  which 
the  water  flowed,  so  that  no  stem  corrections  were  necessary.  More- 


226  J.  W.  HORNBECK. 

over,  these  thermometers  were  placed  so  that  their  bulbs  were  at  exactly 
equal  distances  from  the  points  C  and  D  respectively.  The  tubes  leading 
from  the  jacket  to  the  thermometers  were  made  as  short  as  possible 
and  were  packed  each  with  the  same  number  of  layers  of  asbestos  paper. 
Likewise,  the  glass  tubes  containing  the  thermometers  were  packed 
similarly  so  that,  even  though  the  two  indicated  temperatures  which 
differed  considerably  when  working  far  from  room-temperature,  still 
the  arithmetic  mean  of  the  two  readings  gave  the  true  mean  temperature 
of  the  water  in  the  jacket. 

The  space  surrounding  the  tube  within  the  brass  jacket  was  packed 
tight  with  cotton  wool  and  the  outside  surface  of  the  jacket  was  wrapped 
with  fourteen  layers  of  heavy  cotton  flannel. 

Galvanometer. — The  galvanometer  used  was  of  the  D'Arsonval  type 
and  designed  especially  for  work  with  thermo-couples.  It  has  a  resist- 
ance of  230  ohms,  a  period  of  four  seconds,  and  a  sensibility  of  210 
megohms  for  a  scale  distance  of  I  meter.  By  means  of  an  unusually 
good  lens,  however,  the  image  of  a  lamp  filament  was  brought  to  a  sharp 
focus  on  a  scale  5^  meters  distant  from  the  mirror.  At  5^  meters 
the  sensibility  was  8.6  X  icr10  amperes  per  millimeter  deflection.  The 
E.M.F.  of  the  copper-constantan  thermo-couples  was  about  40  micro- 
volts per  degree,  giving  deflection  of  0.2  mm.  per  i/iooo  degree.  Thus 
a  change  in  temperature  of  one  thousandth  of  a  degree  could  be  detected. 

Ammeters  and  other  Apparatus. — Except  for  the  potassium  tube, 
where  the  value  of  the  heating  current  sometimes  exceeded  150  amperes, 
a  new  Siemens  and  Halske  ammeter  was  used.  It  was  standardized  by 
means  of  a  Wolff  potentiometer,  Weston  standard  cell,  and  a  standard 
o.oi  ohm  resistance.  For  the  data  on  potassium  a  Weston  direct  reading 
ammeter  (0-200)  was  used.  This  was  put  in  series  with  the  new  ammeter, 
mentioned  above,  and  calibrated  for  the  range  over  which  it  was  used. 

All  of  the  standard  thermometers  except  No.  17,481  were  standardized 
at  the  Reichsanstalt.  No.  17,481  was  certified  by  the  Bureau  of  Stand- 
ards. These  thermometers  were  graduated  to  tenths  of  a  degree. 

An  Otto  Wolff  potentiometer,  Otto  Wolff  resistance  boxes,  and  a 
Weston  standard  cell  were  used. 

The  heating  current  was  supplied  by  the  department  storage  battery. 

Arrangement  of  the  Electrical  Apparatus. — The  potentiometer,  P,  was 
connected  as  shown  in  Fig.  5.  B\  was  a  small  storage  cell;  B%,  the 
standard  cell;  RI,  R%  and  R$  were  resistance  boxes.  By  adjusting  Rs  at 
the  beginning  of  a  run,  the  potential  difference  from  A  to  C  was  made 
equal  to  the  E.M.F.  of  the  standard  cell.  RI  and  R2  were  kept  constant. 

The  switches  and  keys  of  the  potentiometer  circuit  which  had  to  be 


VOL.  Ill 
No.  3.    J 


CONDUCTIVITIES   OF   ALKALI   METALS. 


227 


operated  continually  while  taking  readings,  were  grouped  together  on 
one  switchboard  shown  diagrammatically  in  Fig.  6.     C\  and  C%  represent 


B, 


0     O 
O     0 


O     O 
O     O 

o    o 


O  0 
0  0 
0  0 


Fig.  5. 


Fig.  6. 


commutators  of  the  rocker  type;  Si,  52  and  53  were  two-way  switches  of 
the  rocker  type;  K2  and  K%  were  ordinary  mercury  keys.  Six  blocks  of 
paraffine  were  mounted  upon  a  glass  plate,  30  X  40  cm.,  in  the  positions 
indicated.  The  thirty- two  mercury  wells  which  were  sunk  in  the  paraf- 
fine, were  all  lined  by  small  glass  cups  which  served  as  supports  for 
the  metal  rockers.  These  rockers  were  all  made  of  copper  and  only 
copper  wires  dipped  into  the  mercury  cups,  all  being  wound  from  the 
same  spool.  In  this  way,  contact  potential  differences  were  reduced  to 
a  minimum. 


Fig.  7. 

Fig.  7  shows  a  diagram  of  the  exact  connections  of  the  electric  circuits 
and  the  relative -positions  of  the  apparatus,  with  the  exception  of  the 
galvanometer  which  was  on  a  wall  bench  on  the  opposite  side  of  the  room, 
meters  away.  The  ammeter,  A.M.,  commutator  Cf,  controlling 


228  J.  W.  HORNBECK. 

resistance  R',  and  key  K" ,  were  all  within  easy  reach  of  the  observer. 
K"  was  a  short-circuiting  key  to  avoid  arcing  when  the  rocker  of  Cr  was 
thrown  over.  jR4  was  simply  a  protective  resistance  for  the  galvanometer 
and  standard  cell,  and  could  be  cut  out  of  the  circuit  by  a  suitable  plug. 

IV.  EXPERIMENTAL  DETAILS. 

Construction  of  Thermo-couples. — Since  the  alkali  metals  dissolve  ordi- 
nary solder,  it  could  not  be  used  for  the  junctions  which  were  placed  in 
the  tubes.  Moreover,  it  was  not  an  easy  matter  to  hard-solder  the  junc- 
tions without  burning  the  minute  copper  wires.  Several  attempts  to 
do  this  having  failed,  it  was  decided  to  try  the  use  of  mechanical  contacts. 
The  fine  copper  wire,  0.12  mm.  in  diameter,  was  wound  around  the  con- 
stantan  wire  (diam.  0.18  mm.)  for  a  distance  of  about  2  mm.  The  shape 
of  these  junctions  was  admirably  adapted  to  the  double  purpose  of  meas- 
uring both  the  temperature  and  potential  difference  between  two  cross- 
sections.  They  were  mounted  in  a  tube  of  sodium-potassium  alloy  but 
the  data  was  inconsistent  and  on  removing  the  junctions  from  the  tube 
and  attempting  to  check  their  calibration,  it  was  found  that  two  of  the 
three  calibration  curves  had  shifted  by  an  amount  equivalent  to  more 
than  one  tenth  of  a  degree. 

So  it  was  considered  necessary  to  solder  the  wires  together.  The 
method  which  finally  succeeded  was  as  follows.  Nearly  equal  weights 
of  copper  and  silver  were  melted  together  with  a  small  blast  flame.  A 
junction  formed  by  two  or  three  turns  of  the  copper  wire  around  the 
constantan,  was  moistened  and  covered  with  powdered  borax.  Then, 
at  a  time  when  the  temperature  of  the  silver-copper  alloy  was  just  above 
the  melting  point,  the  junction  was  dipped  beneath  the  surface  of  the 
globule  and  quickly  removed. 

Junctions  could  be  soldered  in  this  way  without  any  injury  to  the 
delicate  wires.  Such  junctions,  therefore,  were  used  in  the  last  three 
tubes  experimented  upon, — the  three  for  which  the  data  are  given  in  this 
paper.  The  ice  junctions  were  soldered  with  ordinary  soft-solder.  - 

For  the  alloy  tube  and  the  potassium  tube,  copper  wire  0.12  mm.  in 
diameter  was  used.  However,  it  was  found  to  be  almost  impossible 
to  go  through  the  long  process  of  calibrating  the  thermo-couples,  mount- 
ing them  into  the  tube,  filling  the  tube,  and  finally  mounting  the  tube 
between  the  water-baths,  without  breaking  one  of  these  frail  wires  at 
some  point  where  it  could  not  be  soldered, — thus  involving  the  loss  of  the 
thermo-couple  and  several  days'  work.  Consequently,  somewhat  larger 
copper  wires  were  used  in  the  sodium  tube.  In  this  case  the  diameter 
of  the  wire  was  0.16  mm.  It  can  be  shown,  however,  that  the  error  due 


CONDUCTIVITIES   OF   ALKALI    METALS.  22<) 

to  the  conductivity  of  this  wire  was  negligible  for  the  conditions  under 
which  it  was  used.  For  all  three  of  the  tubes  the  constantan  wire  used 
had  a  diameter  of  0.18  mm. 

Platinum-constantan  thermo-couples  were  used  in  the  lead  rod  be- 
cause, at  that  time,  it  was  thought  platinum  wire  would  be  used  in  the 
case  of  the  alkali  metals  since  it  could  be  sealed  into  the  glass,  but  the 
plan  proved  impracticable. 

Calibration  of  the  Thermo-couples. — The  thermo-j unctions  and  ther- 
mometer were  mounted  within  a  large  Dewar  flask  which  contained  also 
a  rotary  stirrer.  For  the  lower  temperatures  salt  and  ice  were  used  to 
keep  the  temperature  from  rising,  while  for  the  higher  temperatures 
steam  was  introduced  slowly  through  a  small  tube  near  the  wall  of  the 
flask  at  a  point  diametrically  opposite  the  position  of  the  thermo-j  unctions 
and  thermometer.  The  temperature  in  this  way  could  be  held  very 
steady  by  regulating  the  gas  pressure  of  the  three  Bunsen  flames  which 
heated  the  boiler.  The  rotary  stirrer  was  run  by  a  small  motor. 

For  the  first  few  calibration  curves  a  cathetometer  was  used  to  read 
the  thermometer  scale.  This,  of  course,  was  a  most  accurate  method, 
but  it  involved  the  difficulty  of  holding  the  temperatures  constant  for 
several  minutes  at  a  time,  since  the  vernier  had  to  be  adjusted  and  read 
both  before  and  after  balancing  the  potentiometer  for  direct  and  reversed 
currents.  Consequently,  it  was  decided  to  try  a  direct-reading  eye-piece 
attached  to  the  stem  of  the  thermometer.  By  this  method  the  data  for 
a  point  on  the  calibration  curve  could  be  obtained  so  much  more  quickly 
that  the  loss  in  accuracy  of  the  scale  reading  was  almost  compensated  by 
the  gain  in  time  and  consequent  smaller  variation  in  the  temperature. 
Readings  were  taken  at  intervals  of  about  one  or  two  tenths  of  a  degree 
over  the  particular  range  where  the  curves  were  to  be  used  and,  when  the 
points  were  plotted,  there  was  no  doubt  about  the  proper  position  of  the 
line. 

The  curves  obtained  in  this  way  were  reliable  to  about  three  or  four 
thousandths  of  a  degree,  for  the  measurement  of  temperature  differences; 
and,  since  this  was  as  high  a  degree  of  accuracy  as  was  required  in  the 
calibration,   the   use  of   the   cathetometer  was 
abandoned  in  favor  of  the  quicker  and  less  la-     ^11  Q          g        ^ 
borious  procedure.  _Jl— J! li 11 


Preparation  of  the  Tubes. — The  kind  of  tube 
used  to  contain  the  alkali  metals  is  shown  in  Fig-  8- 

Fig.  8.    The  side  tubes  A ,  B  and  C,  through  which 

the  thermo-j  unctions  were  introduced,  were  about  2  mm.  in  diameter 
and  10  cm.  apart.     They  were  sealed  on  in  such  a  way  as  to  change  the 


23O  J.  W.  HORNBECK. 

cross  section  of  the  main  tube  as  little  as  possible.  The  filling  tube  D 
was  always  placed  at  least  4  cm.  from  C.  The  diameters  of  the  tubes 
are  given  in  the  data  tables.  The  entire  length  in  each  case  was  about 
30  cm. 

Considerable  difficulty  was  met  in  devising  a  method  of  sealing  in 
the  thermo-j  unctions  so  that  a  vacuum  could  be  maintained  at  tempera- 
tures above  the  melting  point  of  sealing  wax.  It  was  finally  accom- 
plished in  the  following  way.  The  two  wires  of  the  junctions,  one  of 
which  in  each  case  was  contained  in  a  minute,  slightly  funnel-shaped 
glass  tube  for  insulation  purposes,  were  first  sealed  into  the  tube  by  means 
of  "Quixo  Caementium."  This  is  a  mineral  cement,  a  commercial 
article,  which  was  purchased  from  one  of  the  local  dealers.  It  dries  very 
hard  but  it  is  somewhat  porous  and  will  hold  a  vacuum  only  a  short  time. 
Consequently,  after  the  caementium  had  dried  it  was  covered  over  with 
a  layer  of  sealing  wax.  A  kind  called  De  Khotinsky  cement  was  used 
because  it  has  a  higher  melting  point  than  the  red,  "Bank  of  England" 
wax.  The  caementium  held  the  thermo-j  unctions  rigidly  in  their  posi- 
tions and  when  the  tube  was  heated  the  air  pressure  could  not  force 
the  soft  wax  into  the  tube. 

After  grinding  the  ends  of  the  tube  they  were  fitted  into  circular  grooves 
in  the  copper  end-disks,  about  1.5  mm.  deep.  These  joints  were  filled 
with  litharge  (PbO)  mixed  in  boiled  linseed  oil,  and  baked  for  several 
hours  at  a  temperature  of  about  100°  C.  When  thoroughly  dry  and  solid 
they  were  covered  with  a  thick  layer  of  the  Khotinsky  sealing  wax. 
The  reason  for  using  litharge  in  place  of  caementium,  for  sealing  on  the 
end  discs,  was  the  fact  that  it  does  not  dissolve  in  water, — thus  reducing 
the  fire-risk  in  case  of  accident. 

Before  the  end  discs  were  sealed  on,  an  accurate  scale  was  introduced 
within  the  tube  and  the  thermo-j  unctions  bent  into  positions  which  spaced 
them  exactly  10  cm.  apart.  They  extended  about  3  mm.  into  the  tube. 

The  sodium  and  potassium  tubes  were  prepared  as  described  above. 
Sealing  wax  alone,  however,  was  used  in  the  case  of  the  sodium-potassium 
alloy  and  for  this  reason  no  data  could  be  taken  with  this  tube  for  tem- 
peratures above  45°. 

Filling  the  Tubes. — The  method  of  filling  the  tubes  is  illustrated  in  Fig. 
9.  The  sodium  or  potassium  was  introduced  into  the  bulb  D  through  an 
opening  at  G.  The  tube  was  then  sealed  at  G  and  the  Gaede  pump 
started.  After  melting  the  metal,  it  was  kept  hot  for  an  hour  or  more 
during  the  exhaustion,  in  order  to  drive  off  all  traces  of  the  oil.  When 
the  crust  finally  appeared  dry  and  black,  and  the  discharge  tube  F  showed 
only  the  presence  of  the  alkali  vapor,  the  system  was  sealed  off  at  E. 


No's"']  CONDUCTIVITIES  OF  ALKALI   METALS. 

Then,  holding  AB  in  a  horizontal  position  and  keeping  it  hot  with  Bunsen 
flames,  the  tube  D  was  tilted  and  the  bright,  pure  metal  poured  through 
a  system  of  small  funnels  at  C  which  held  back  all  of  the  dross. 

It  was  a  very  difficult  matter  to  fill  a  tube  because  of  the  formation  of 
bubbles  due  to  vapor  pressure,  and  further,  because  of  the  contraction 
of  the  metal  on  cooling.  The  only 
way  it  could  be  done  at  all  was  to 
pour  in  metal  a  little  at  a  time  and 
allow  it  to  solidify  before  adding 
any  more.  Thus  it  was  necessary 
to  melt  the  successive  portions  to- 
gether to  avoid  layers  and  this  local 
heating  often  involved  the  loss  of 
a  tube,  either  by  breaking  the  glass  Fig.  9. 

or  by  letting  the  air  in  through  the 

softened  cement  at  one  of  the  thermo- junctions.  When  filled,  the  tube 
AB  was  sealed  off  at  a  stricture  H  and  it  was  then  ready  to  be  mounted 
between  the  water-baths. 

Purity  of  the  Metals. — The  sodium  and  potassium  were  purchased  from 
Eimer  and  Amend  and,  in  a  personal  letter  from  the  company,  were 
claimed  to  be  ''very  pure."  I  am  indebted  to  Dr.  G.  McP.  Smith,  of  the 
chemistry  department,  for  the  following  test  on  the  purity  of  these  metals. 

Sodium.  i 

1.  Free  from  iron  (KCNS  test). 

2.  Free  from  calcium  ((NH4)2C2O.i  test). 

3.  Free  from  magnesium  (NaaHPCh  test). 

4.  Free  from  aluminum  (no  ppt.  with  NH4OH-Na2HPO4  test). 

5.  Free  from  potassium  (H2PtCle  test). 

Spectroscopic  test  also  negative,  but  conditions  were  not  most  favorable  at  time  of  test. 

Potassium. 

1.  Free  from  iron. 

2.  Free  from  calcium. 

3.  Free  from  magnesium. 

4.  Free  from  aluminum. 

5.  Contains  enough  sodium  to  give  a  test  with  the  spectroscope.     Undoubtedly  only  a 

trace. 

Method  of  Control  of  Temperatures. — The  apparatus  for  controlling 
temperatures  has  been  described  in  Chapter  III.  For  the  determinations 
above  room  temperature,  the  temperatures  were  adjusted  and  held 
constant  by  means  of  Bunsen  flames,  one  under  each  end-bath  and  three ' 
beneath  the  large  reservoir  from  which  the  water  was  pumped  through 
the  brass  jacket.  For  the  lower  temperatures  the  turbine  was  discarded 
and  cold  water  was  run  through  the  jacket  by  gravity  pressure,  the  rate 


232 


J.  W.  HORNBECK. 


FSECOND 

LSERIES. 


of  flow  being  regulated  by  a  small  globe  valve.  In  these  determinations 
the  temperatures  of  the  end  baths  were  watched  constantly  by  a  student 
helper  and  were  maintained  by  the  continuous  addition  of  snow  and  salt. 


Fig.  10. 

Regulation  of  the  Heating  Current. — As  already  mentioned,  the  currents 
from  the  large  storage  battery  were  remarkably  constant.  The  slight 
regulation  necessary  was  accomplished  with  a  mercury  rheostat.  The 
U-tube,  which  was  made  of  glass  tubing  2.6  cm.  in  diameter,  stood  80  cm. 
high.  Continuous  adjustments  could  be  made  by  varying  the  position 
of  the  copper-plated  iron  rods  which  dipped  into  the  mercury. 

V.   DATA  TABLES  AND  CURVES. 

In  order  to  cut  down  the  length  of  the  paper  the  original  data  will  be 
given  only  for  a  few  typical  runs.  They  will  serve  to  illustrate  the  method 


&^1 


'  ohm 


30 


70  90 


le.  777  f>  c  r  at  o  r  e. 

Fig.  11. 

of  taking  observations  and  to  indicate  the  degree  of  consistency  obtained 
at  different  temperatures.  In  the  tables  which  follow  these  "specimen 
runs,"  merely  the  final  results  are  recorded. 


VOL.  II.] 
No.  3.   J 


CONDUCTIVITIES   OF   ALKALI   METALS. 


233 


Meaning  of  Symbols. — In  all  the  data  tables  the  following  notation 
is  used: 

rlt  rz  =  balance-resistance  on  potentiometer  dial  for  thermo-couples 

No.  i  and  No.  3. 
rz  =  balance-resistance  for  thermo-couple  No.  2  at  middle  of  tube 

(or  rod). 
r'  =  balance-resistance  when  reading  P.D. 


~7e  fn  p  c  t-a.'tvTr  e 

Fig.  12. 

«i,  w2,  u3  =  temperatures  corresponding  to  resistances  rlt  rz,  rs. 
UQ  =  temperature  of  the  brass  jacket. 


tm  =  %(u'  +  ^2)  =  temperature  for  which  the  values  of  <r/X,  p  and 
X  are  taken  in  plotting  curves. 


Fig.  13. 

V  =  one  half  of  the  P.D.  between  the  two  points  which  were  held 
at  the  same  temperature. 


234 


J.  W.  HORNBECK. 


[SECOND 

[SERIES. 


I  —  value  of  heating  current  in  amperes. 
A  =  U2  -  u' .  U  =  A  -  eN. 

N  =  WQ  —  u2  +  J/Q&.  e  =  A/N  when  /  =  o. 

The  letters  D  and  R  in  the  tables  represent  direct  and  reversed  currents 
through  the  potentiometer  to  eliminate  contact  potential  differences. 

No.  2606  and  No.  2607  refer  to  the  two  Beckmann  thermometers  which 
gave  the  temperature  of  the  brass  jacket. 


TABLE  I. 

Constants  for  the  Three  Tubes. 


Substance. 

Inside  Diameter. 

Area  a. 

Effective  Length  /. 

Na-K  Alloy  

1.562  cm. 

1.916 

20  cm 

Potassium  

1.620  cm 

2  061 

20  cm 

Sodium 

1  234  cm 

1  196 

20  cm 

p  =  —  =  .0958^?  =  —  — - — '•  — ,  for  sodium-potassium  alloy. 

0.103  X  2V    . 
P  =  —  — ,  for  potassium  tube. 

.0598  X  2V 
P  -  —  — — ,  for  sodium  tube. 

TABLE  II. 

Correction  Factor  for  Potassium  Tube  (Specimen  Run). 


»1 

*"8 

r* 

«o  No.  six. 

«0  No.  212. 

D 
R 

187.8 
186.8 

187.7 
186.8 

197.2 
196.2 

2.20 

1.36 

D 
R 

187.5 
186.6 

187.8 
186.9 

197.0 
196.2 

2.18 

1.35 

D 
R 

187.5 
186.7 

187.8 
186.9 

197.0 
196.3 

2.19 

1.30 

D 
R 

187.5 
186.7 

187.6 
186.7 

196.9 
196.2 

2.20 

1.27 

D 
R 

187.1 
186.4 

187.8 
186.9 

196.9 
196.1 

2.23 

1.24 

Left  bath  held  at  18.4°;  right  bath  at  18.3°. 

Mean  temperature  on  No.  211  =  2.20  +  33.06  =  35.26°. 

Mean  temperature  on  No.  212  =  1.30  +  32.91  =  34.21°. 

«o  =  H(35.26  +  34-21)  =  34-74°  C. 

Mean  n  =  187.1  ohms;  u\  =  20.025°. 

Mean  n  =  187.3  ohms;  ut  =  19.965°. 

Mean  rz  =  196.6  ohms;  uz  =  20.925°. 

A  =  20.925  —  19.955  =  0.930°. 

N  =  34.74  -  20.925  +  0.155  =  13.97°- 

_  A  _  0.930 

~  N~  13.97 


.066. 


VOL.  II.] 
No.  3.   J 


CONDUCTIVITIES    OF   ALKALI    METALS. 


235 


TABLE  III. 

Sodium-Potassium  Alloy  at  5.7°  (Specimen  Run). 


Main  Current  Direct. 

Main  Current  Reversed. 

r' 

n 

^-3 

r* 

»0  No.  3606. 

MO  No.  2607. 

n 

fa 

rt 

r1 

D 

33.9 

35.9 

68.4 

4.05 

4.30 

34.9 

35.7 

68.8 

R 

3667 

35.2 

37.3 

69.8 

4.10 

4.25 

36.2 

37.2 

70.2 

3661 

D 
R 

3656 

34.2 
36.0 

35.9 
37.3 

68.5 
69.9 

3.95 
3.95 

4.15 
4.20 

34.9 
36.7 

35.6 
37.2 

68.4 
70.3 

3664 

D 
R 

3656 

34.2 
36.0 

35.9 
37.4 

68.6 
70.0 

3.94 
3.90 

4.20 
4.15 

34.8 
36.8 

35.5 
37.2 

68.4 
70.4 

3661 

D 
R 

3657 

34.2 
36.1 

35.9 
37.6 

68.4 
70.2 

3.95 
3.93 

4.15 
4.15 

34.6 
36.6 

35.4 
37.2 

68.2 
70.2 

3663 

D 
R 

3658 

34.1 
35.9 

35.7 
37.6 

68.3 
70.1 

3.98 
3.93 

4.17 
4.15 

34.6 
36.6 

35.4 
37.2 

68.1 
70.1 

3662 

Left  bath  at  —  0.4°;  right  bath  at  o°. 

6  volts,  6  sets  in  parallel.     /  =41.2  amp. 

Mean  r\  =  35.4  ohms;  u\  =  4.02°.     Mean  reading  on  No.  2606  =  3.97. 

Mean  n  =  36.6  ohms;  us  =  4.04°.     Mean  reading  on  No.  2607  =  4.20. 

Mean  rz  =  69.3  ohms;  uz  =  7.42°. 

Mean  temp,  on  No.  2606  =  3.97  + 

Mean  temp,  on  No.  2607  =  4.20  -f- 

MeanV  =  3,660  ohms.     2V  =  3660  X  4  X  io~6  =  .01464  volt. 

Sample  Calculation. 

A  =  7.42  —  4.03  =  3.39.     tm  =  M(4-03  +  7-42)  =  5-7°. 
N  =  MO  —  uz  +  HA  =  6.67  —  7.42  +  0.57  =  —  0.18. 
U  =  A  —  tZV  =  3.39  +  0.22  X  0.18  =  3.43. 

£  =  2U  =      6.86 

X  " 


V*       (.00732)2 
.0958  X  .01464 

41.2 

io5 


=  128.1  X  io3. 
=  34040  X  io~9  ohm. 
=  .0547  cal. 


4.19  X  128.1  X  3404 

TABLE  IV. 

Sodium  at  Room  Temperature  (Specimen  Run). 


Main  Current  Direct. 

Main  Current  Reversed. 

n 

r& 

''a 

r' 

«0  No.  2606. 

«o  No.  2607. 

n 

r» 

ft 

r' 

D 

R 

187.6 
187.0 

190.9 
190.3 

218.0 
217.4 

3096 

5.40 

5.48 

187.6 
188.7 

188.9 
188.0 

217.1 
217.9 

3099 

D 
R 

188.3 
187.3 

190.5 
189.6 

218.0 
217.2 

3093 

5.43 

5.52 

187.7 
189.5 

188.9 
187.9 

217.3 
218.2 

3098 

D 
R 

188.7 
187.7 

190.9 
190.3 

218.6 
217.6 

3093 

5.48 

5.56 

188.2 
189.3 

189.0 
188.2 

217.6 
218.4 

3098 

D 
R 

188.2 
187.4 

190.9 
190.2 

218.5 
217.5 

3093 

5.53 

5.61 

188.1 
189.4 

188.9 
188.1 

217.4 
218.2 

3098 

12  volts,  12  sets  in  parallel.     /  =  146.3  amp. 
Left  bath  held  at  14.8°;  right  bath  held  at  15.9°. 


236 


J.  W.  HORNBECK. 


[SECOND 

[SERIES. 


Mean  n  =  188.2;  u\  =  20.08°.     Temp,  on  No.  2606  =  5.46  +  18.08  =  23.54. 

Mean  rz  =  189.5;  ««  =  20.12°.     Temp,  on  No.  2607  =  5.54  +  18.05  =  23.59. 

Mean  rz  =  217.8;  uz  =  23.01.     uo  =  23.57°  C. 

Mean  r'  =  3,096  ohms.     2V  =  3,096  X  4  X  io~8  =  .01238  volt. 

A  =  2.91.     N  =  1.05.     U  =  2.85°.     tm  =  21.5°. 

TABLE  V. 

Potassium  at  57.8°  (Specimen  Run). 


Main  Current  Direct. 

Main  Current  Reversed. 

r' 

n 

r* 

2 

#o  No.  2606. 

«0  No.  0607. 

n 

$ 

rz 

r' 

D 

560.6 

554.4 

584.5 

3.38 

2.75 

557.6 

558.4 

584.4 

R 

3075 

559.0 

556.2 

582.6 

3.37 

2.76 

556.0 

559.8 

583.0 

3070 

D 

556.0 

553.5 

582.8 

3.38 

2.76 

555.7 

557.9 

583.6 

R 

3071 

557.8 

555.2 

581.0 

3.42 

2.77 

553.8 

559.6 

582.0 

3070 

D 

3078 

557.4 

554.9 

584.1 

3.43 

2.78 

557.7 

557.6 

584.3 

R 

558.9 

556.7 

582.3 

3.48 

2.81 

555.4 

559.7 

582.4 

D 

3078 

553.6 

555.9 

584.3 

3.42 

2.83 

558.1 

555.3 

584.3 

3079 

R 

555.3 

560.6 

582.5 

3.35 

2.81 

555.6 

557.1 

582.4 

D 

3074 

554.4 

555.9 

584.4 

3.27 

2.73 

557.8 

555.2 

584.0 

3074 

R 

556.2 

558.6 

582.6 

3.25 

2.70 

555.4 

557.0 

582.2 

16  volts,  8  sets  in  parallel.     /  =  148.1  X  1.026  =  152.0  amp. 

Left  bath  at  51.0°.     Right  bath  at  51.3°. 

Mean  n  =  556.6;  u\  =  56.625°.     Temp,  on  No.  2606  =  3.38  +  54.98  =  58.36. 

Mean  n  =  557-4;  «»  =  56.630°.     Temp,  on  No.  2607  =  2.77  +  55.13  =  57-po- 

Mean  rz  =  583.2;  uz  =  59-070°.     uo  =  58.13°. 

Mean  r'  =  3074  ohms.     2V  =  .012296  volt. 

A  =  2.443°.     N  =  -  0.53.     U  =  2.478°.     tm  =  57.8°. 

TABLE  VI. 

Values  of  Correction  Factor  e. 


Substance. 

«0 

«2 

A 

tf 

6 

Lead  rod 

21  7 

16    7 

0918 

5  38 

0  171 

Na-K  alloy  

21.19 

15.40 

1.35 

6.01 

0.224 

Potassium 

24.46 
34  74 

19.86 
20925 

1.02 
0930 

4.77 
13  970 

0.214 
0066 

.Sodium  .  . 

41.80 

18.66 

1.38 

23.37 

0.059 

TABLE  VII. 

Complete  Results  for  Lead  (Commercially  Pure) . 


Run 
No. 

MO 

«2 

tm 

aF 
io-5  x 

A 

N 

u 

/ 

Amp. 

a/A. 
I03X 

1 

21.64 

21.94 

20.6 

1253 

2.671 

0.14 

2.647 

51.0 

134.6 

2 

21.65 

23.60 

21.7 

1566 

3.838 

-1.32 

4.062 

63.3 

132.5 

3 

21.71 

23.28 

21.3 

1588 

4.046 

-0.90 

4.199 

64.3 

133.2 

Remark. — For  run  No.  3,  the  lead  rod  was  inside  of  a  close-fitting  glass  tube. 


VOL.  II.1 
No.  3.   J 


CONDUCTIVITIES  OF   ALKALI   METALS. 


237 


TABLE  VIII. 

Complete  Results  for  Sodium-Potassium  Alloy. 
(Masses  taken  proportional  to  the  atomic  weights.) 


Run 
No. 

«0 

«2 

tm 

«F 

10-6  X 

A 

N 

u 

/ 

Amp. 

<7/A 

io»X 

p  Ohm 

10-8  X 

A 
Cal. 

1 

-8.30 

-8.28 

-10.6 

1511 

4.56 

+0.74 

4.40 

66.0 

154.4 

2193 

.0705 

2 

-9.40 

-6.37 

-  8.9 

1682 

5.00 

-2.20 

5.48 

72.9 

155.2 

2210 

.0696 

3 

+6.67 

7.42 

5.8 

1464 

3.39 

-0.18 

3.43 

41.2 

128.1 

3404 

.0547 

4 

6.66 

8.07 

6.2 

1588 

3.83 

-0.77 

4.00 

44.6 

127.0 

3411 

.0551 

5 

22.40 

23.936 

22.0 

1684 

3.931 

-0.88 

4.122 

45.9 

116.3 

3515 

.0584 

6 

22.54 

24.075 

22.1 

1702 

4.003 

-0.86 

4.190 

46.2 

115.9 

3527 

.0584 

7 

22.66 

22.395 

20.7 

1500 

3.453 

+0.84 

3.271 

40.9 

116.2 

3513 

.0585 

8 

43.90 

44.54 

42.9 

1550 

3.17 

-0.11 

3.19 

40.8 

106.1 

3640 

.0619 

TABLE  IX. 

Complete  Results  for  Potassium. 


Run 
No. 

«o 

* 

5.0 

aF 
xo-6  x 

A 

N 

u 

Amp. 

<r/A 
io*  x 

p  Ohm 
10-8  x 

A 
Cal. 

1 

5.91 

5.790 

881 

1.557 

+0.38 

1.531 

141.9 

158.2 

649.2 

0.232 

2 

6.58 

5.810 

5.0 

862 

1.525 

+  1.02 

1.454 

137.9 

156.5 

644.2 

0.237 

3 

21.16 

21.670 

20.7 

1035 

1.965 

-0.18 

1.978 

151.6 

147.7 

703.5 

0.230 

4 

21.22 

21.590 

20.6 

1030 

1.920 

-0.05 

1.923 

151.2 

145.1 

701.5 

0.234 

5 

21.45 

21.675 

20.9 

932 

1.603 

+0.04 

1.600 

137.6 

147.4 

698.0 

0.232 

6 

58.13 

59.070 

57.8 

1230 

2.443 

-0.53 

2.478 

152.0 

131.1 

833,8 

0.218 

7 

57.91 

58.510 

57.4 

1184 

2.312 

-0.21 

2.326 

147.3 

132.4 

835.3 

0.216 

TABLE  X. 

Complete  Results  for  Sodium. 


Run 
No. 

«0 

«2 

tm 

aF 

10-5  X 

A 

N 

U 

7 
Amp. 

a/A 
io»X 

p  Ohm 

10-8  x 

A 

Cal. 

1 

7.20 

6.97 

5.7 

1152 

2.68 

+0.68 

2.64 

147.7 

159.0 

466.4 

0.321 

2 

7.75 

7.22 

5.8 

1176 

2.82 

+  1.00 

2.76 

150.7 

159.5 

466.7 

0.321 

3 

23.42 

22.12 

20.9 

1110 

2.385 

+  1.70 

2.283 

130.6 

148.2 

508.3 

0.317 

4 

23.57 

23.01 

21.5 

1238 

2.91 

+  1.05 

285 

146.3 

148.8 

506.0 

0.317 

5 

43.32 

43.44 

42.1 

1207 

2.57 

+0.31 

2.55 

128.3 

139.7 

562.6 

0.304 

6 

44.97 

43.38 

41.7 

1360 

3.32 

+2.14 

3.19 

145.5 

138.1 

559.0 

0.309 

7 

62.30 

62.84 

61.3 

1390 

3.15 

+0.01 

3.15 

137.2 

130.4 

605.8 

0.302 

8 

63.11 

62.83 

61.4 

1320 

2.93 

+0.77 

2.88 

130.7 

132.1 

eo4.o 

0.299 

9 

89.01 

89.43 

88.1 

1309 

2.67 

+0.03 

2.67 

118.0 

124.8 

663.4 

0.288 

VI..  DISCUSSION  OF  RESULTS. 

In  using  the  experimental  method  of  obtaining  the  value  of  the  correc- 
tion factor  €  for  the  alkali  metals,  it  was  necessary  to  assume  that  for 
the  steady  state  the  temperatures  at  corresponding  points  on  the  inside 
and  outside  surfaces  of  the  glass  tube  were  equal;  i.  e.,  that  the  tempera- 


238  J.  W.  HORN  BECK. 

ture  gradient  through  the  walls  of  the  glass  tube  could  be  neglected  in 
comparison  with  the  drop  in  temperature  through  the  cotton  wool.  One 
reason  for  making  the  runs  with  the  lead  rod  was  to  find  out  if  this  as- 
sumption would  introduce  an  error  large  enough  to  be  detected  Table 
VII.  answers  the  question.  The  fact  that  the  value  of  cr/X  for  run  No.  3 
falls  between  those  for  runs  No.  I  and  No.  2,  proves  that  the  effect  of 
surrounding  the  rod  with  the  glass  was  smaller  than  other  experimental 
errors.  Lead  was  chosen  for  this  experiment  because  of  its  low  heat 
conductivity.  The  glass  wall  would  have  a  still  smaller  effect  in  case  of 
the  sodium  and  potassium. 

Another  reason  for  taking  the  data  for  lead  was  to  have  a  means  of 
comparing  my  results  with  those  of  Jaeger  and  Diesselhorst.  In  this 
connection  it  should  be  noted  that  my  average  value  of  <r/X  for  lead  at 
21.5°  is  133.4  X  io3  while  that  of  Jaeger  and  Diesselhorst  for  pure  lead, 
when  reduced  to  21.5°,  is  138.2  X  io3.  This  was  considered  a  good  check 
because  the  lead  I  used  was  only  commercially  pure.  The  presence  of 
impurities  always  reduces  the  value  of  cr/X. 

As  to  accuracy  of  results  it  should  be  pointed  out  that  for  each  run 
steady  conditions  were  held  for  one  to  two  hours  and  readings  were  taken 
continually  during  this  time.  Thus  each  value  of  «i,  #2  and  u^,  used  in 
the  calculations,  depends  upon  sixteen  to  twenty  readings  on  the  poten- 
tiometer, while  the  values  of  V  are  computed  from  the  mean  of  eight  to 
ten  readings.  The  current  could  be  maintained  much  more  nearly 
constant  than  could  the  temperatures  and  therefore  the  potential  dif- 
ference did  not  need  to  be  read  so  often.  Moreover,  with  one  or  two 
exceptions,  every  point  on  the  curves  represents  the  mean  result  of  two  or 
three  independent  runs. 

The  curves  for  X/<r  bend  more  than  was  expected.  It  would  be  interest- 
ing to  know  whether  they  become  straight  lines  at  higher  temperatures. 
Judging  from  the  behavior  of  other  metals,  this  should  be  expected. 
Moreover,  when  X/o-T  is  plotted  against  T,  these  curves  slope  downward 
slightly  with  increasing  temperature  while  Lees's  curves  for  most  of  the 
pure  metals  bend  slightly  upward  at  ordinary  temperatures.  Thus 
sodium  and  potassium,  like  nickel,  are  irregular  in  this  respect.  It 
should  be  noted  that  the  heat  conductivities  of  sodium  and  potassium 
decrease  slightly  with  increasing  temperature,  while  the  heat  conductivity 
of  the  alloy  increases  with  the  temperature.  This  is  the  law  followed  by 
most  metals  and  their  alloys.  The  temperature  coefficients  of  sodium 
and  potassium  are  extremely  high. 

The  mean  values  of  the  specific  resistance  of  sodium  and  potassium  at 
room  temperature  and  the  temperature  coefficients  are  given  below  for 
convenience  of  comparison. 


CONDUCTIVITIES   OF   ALKALI   METALS.  239 

spec.  res.  of  Na  at  21.7°  C.  =  5072  X  io~9  ohm/cm.3, 

spec.  res.  of  K    at  20.7°  C.  =  7010  X  io~» 

temp.  coef.  of  Na  =  .00513,  range  6°  to  88° 

temp  coef.  of  K  =  .00552,  range  5°  to  58° 

Northrup's  Results. 

spec.  res.  of  Na  at  20°  C.  =  4873  X  io~» 

spec.  res.  of  K    at  20°  C.  =7116  X  io~» 

temp.  coef.  of  Na  =  .0053,  range  20°  to  80° 

temp.  coef.  of  K  =  .0058,  range  20°  to  50° 

Matthiesen's  Result. 
spec.  res.  of  Na  at  21.7°  C.  =  4464  X  io~9 

Bernini's  Results. 

spec.  res.  of  Na  at  0.0°          =  4739  X  io~" 
spec.  res.  of  K  at  0.0°  =  6644  X  io~* 

Bernini's  results,  when  reduced  to  room  temperature,  are  found  to  be 
higher  than  mine  and  Northrup's,  while  Matthiessen's  value  is  seen  to 
be  lower.  It  is  thought  that  my  results  agree  with  Northrup's  as  closely 
as  could  be  expected,  considering  the  wide  difference  in  method.  Indeed 
his  method  is  the  more  accurate  one  for  electrical  conductivity.  Conse- 
quently, the  results  of  this  investigation  may  be  said  to  confirm  North- 
rup's work  on  the  resistance  of  sodium  and  potassium.  The  slightly 
smaller  values  of  the  temperature  coefficients  suggest  that  the  metals 
used  in  this  work  may  not  have  been  quite  as  pure  as  those  Northrup 
used. 

SUMMARY. 

1.  The  electrical  conductivities  of  sodium,  potassium  and  sodium- 
potassium  alloy  have  been  measured  and  the  results  are  in  agreement 
with  the  values  obtained  by  Northrup. 

2.  The  heat  conductivities  of  the  alkali  metals  have  been  measured  for 
the  first  time,  as  far  as  known. 

3.  The  temperature  coefficients  of  these  conductivities  have  been 
determined. 

4.  The  resistance-temperature  coefficients  of  potassium  and  sodium 
are  extremely  high. 

5.  The  values  of  the  ratio  <r/X  for  the  alkali  metals  are  extremely  high. 

6.  The  alkali  metals  behave  in  no  exceptional  way  as  regards  the 
absolute  values  of  the  thermal  and  electrical  conductivities  at  ordinary 
temperatures. 

7.  As  a  check  on  the  method,  the  ratio  <r/X  was  determined  for  lead 
at  room  temperature  and  the  value  agrees  with  the  one  obtained  by 
Jaeger  and  Diesselhorst. 

8.  A  modification  of  the  electron  theory  of  metallic  conduction  has 


240  J.  W.  HORNBECK.  ]JSS£. 

been  suggested  which  accounts  for  the  variation  of  the  specific  heat  with 
the  temperature,  and  also  explains  the  curves  which  Lees  obtained  for 
the  ratio  X/trT1  for  the  pure  metals  at  low  temperatures. 

In  conclusion,  I  wish  to  acknowledge  my  indebtedness  to  Professor 
A.  P.  Carman,  who  has  followed  this  work  with  continued  interest, 
placing  at  my  disposal  all  the  facilities  necessary  for  the  investigation; 
and  to  Professor  Jakob  Kunz,  under  whose  direction  the  work  was  done, 
for  many  good  suggestions  and  for  invaluable  assistance  in  filling  the 
tubes.  I  also  wish  to  thank  Dr.  G.  McP.  Smith,  of  the  chemistry 
department,  who  analyzed  the  metals  used  in  this  investigation. 

LABORATORY  OF  PHYSICS,  . 

UNIVERSITY  OF  ILLINOIS, 
May,  1913. 

Note. — Since  this  paper  was  written,  I  note  in  the  April  number  of 
Science  Abstracts,  which  has  just  come,  that  W.  Wien  has  published  an 
article  on  "Electric  Conduction  in  Metals"  based  upon  the  "quanta 
hypothesis."  His  theory  may  be  similar  to  the  modification  suggested 
in  this  paper.  The  article  referred  to  is  not  accessible  in  pur  library. 

J.  W.  H. 


(Reprinted  from  the  PHYSICAL  REVIEW,  N.S.,  Vol.  II.,  No.  4,  October, 


A  DETERMINATION  OF  e/m  AND  v  BY  THE  MEASUREMENT 
OF  A  HELIX  OF  WEHNELT  CATHODE   RAYS. 

BY  J.  B.  NATHANSON. 

TN  1904  A.  Wehnelt1  showed  that  the  output  of  negative  carriers  of 
•*•  electricity  emitted  from  incandescent  Pt,  could  be  enormously 
increased  by  coating  the  Pt  with  a  layer  of  an  alkaline  earth  metal  oxide 
like  CaO.  Using  this  Pt  as  a  cathode,  Wehnelt  determined  e/m  and  v 
for  the  cathode  beam  issuing  from  the  hot  lime.  The  method  employed 
was  the  utilization  of  the  potential  difference  of  discharge  and  the  meas- 
urement of  the  diameter  of  the  circle  into  which  the  rays  were  magnet- 
ically bent.  Wehnelt  obtained  an  average  value  of  1.48  X  io7  for  e/m, 
and  for  v  values  ranging  from  0.16  X  io9  to  1.07  X  io9  cm.  per  second. 
J.  Classen,2  employing  a  photographic  method  for  determining  the  diam- 
eter of  the  circle,  obtained  a  value  of  1.773  X  io7  for  e/m.  C.  T.  Knipp,3 
using  the  method  of  electrostatic  and  magnetic  deflections,  obtained  a 
value  of  1.5  X  io7  for  e/m  and  1.6  X  io9  for  v. 

In  the  present  investigation,  the  method  employed  was  the  utilization 
of  the  principle  of  both  magnetic  and  electrostatic  deflections.  This 
avoids  the  assumption  that  all  of  the  electric  energy  of  the  electric  field 
is  converted  into  kinetic  energy  of  the  moving  particles.  Sir  J.  J.  Thom- 
son4 has  shown  that  when  a  moving  electron  is  projected  into  a  uniform 
magnetic  and  a  uniform  electrostatic  field,  the  lines  of  force  of  both  fields 
being  parallel,  that  the  electron  will  describe  a  helical  path,  the  helix 
being  of  increasing  pitch. 

The  helical  path  in  the  case  of  the  Wehnelt  cathode  rays  was  experi- 
mentally realized  as  follows.  The  rays  were  projected  from  a  Wehnelt 
cathode  in  a  direction  perpendicular  to  the  lines  of  force  of  a  uniform 
magnetic  field.  The  path  assumed  by  the  rays  was  a  circle.  Upon 
application  of  a  uniform  electrostatic  field  whose  direction  coincided  with 
that  of  the  lines  of  magnetic  force,  the  circle  was  drawn  out  into  the  form 
of  a  helix. 

1  Ann.  d.  Phys.,  14,  p.  425,  1904. 

2  Phys.  Zeit.,  9,  No.  22,  p.  762,  1908. 
8  Trans.  A.  I.  E.  E.,  p.  1883,  1912. 

4  Thomson's  Cond.  of  Elec.  through  Gases,  2d  ed.,  p.  112. 


308  J.  B.  NATHAN  SON. 

The  circular  path  of  the  rays  is  given  by  the  equation 

mv2 
Hev  =  — , 

or 


where  H  =  magnetic  intensity,  r  =  radius  of  the  circle. 

The  negative  particles  composing  the  rays,  when  projected  in  a  direc- 
tion perpendicular  to  the  electrostatic  field  of  strength  Z,  will  receive  a 
uniform  acceleration  of  Ze/m  in  the  direction  of  the  field,  so  that  in  time 
t  the  electrostatic  deflection  z  will  be 

S  =  Z^.  -  (2) 

mz 

If  n  is  the  number  of  times  an  electron  has  passed  around  the  helix  in 
the  time  t,  while  experiencing  the  electrostatic  deflection  z,  then  v,  the 
velocity  of  projection  of  an  electron,  is  given  by 

2irrn 

r  =  —  .  (3) 

Evidently  the  time  taken  by  the  electron  to  go  once  around  the  circle 
with  the  constant  velocity  of  projection  v,  is  equal  to  the  time  taken  by 
the  electron  to  pass  once  around  on  its  helical  path  with  a  resultant 
velocity  VR.  Hence 


Substituting  the  value  of  v  from  (i)  into  (4)  and  solving  for  e/m,  we 
have, 


It  was  found  very  early  in  the  investigation  that  the  beam  of  rays 
after  having  passed  the  first  time  around  on  its  helical  path,  would  suffer 
a  deflection  or  distortion  when  repassing  over  the  cathode,  this  deflection 
being  due  to  like  sign  of  both  cathode  and  electrons.  As  a  result  of  this 
deflection,  the  uniformity  of  increase  of  pitch  was  disturbed,  and  it  was 
therefore  deemed  advisable  to  measure  the  electrostatic  deflection  for  the 
first  one  half  turn  only.  Accordingly  equation  (5)  reduces  to 


e_         _T_ 

m~  W-2Z  ~  2dIPz' 

where  V  =    potential  difference  of  electrostatic  plates,  d  =  distance  be- 
tween electrostatic  plates. 


No1"/1']  DETERMINATION  OF  e/m  AND  v.  309 

Eliminating  e/m  from  (i)  and  (4)  and  letting  n  =  1/2,  we  have  for  v, 

V  =  IdWz  (7) 

DESCRIPTION  OF  APPARATUS. 

The  discharge  chamber  consisted  of  a  jar  /,  lying  on  its  side,  21  cm.  in 
diameter  and  18  cm.  deep.  The  mouth  of  the  jar  was  ground  plane  to 
receive  a  square  piece  of  plate  glass  P.  This  was  fitted  on  airtight  by 
means  of  a  mixture  of  equal  parts  of  beeswax  and  resin.  The  plate  glass 
window  permitted  accurate  measurements  to  be  taken  on  the  helix 
without  any  accompanying  optical  distortion. 

The  electrostatic  deflections  were  affected  by  two  parallel  Al  plates, 
A  and  B,  resting  on  an  improvised  glass  support  S.  These  plates  were 
circular,  being  15  cm.  in  diameter.  The  upper  plate  A  was  connected 


Electrostatic 
Battery 


Fig.  1. 

through  a  water  resistance  to  the  (+)  pole  of  the  battery,  the  lower  plate 
B,  being  connected  to  the  (  — )  pole.  With  this  arrangement  the  circle 
could  be  drawn  out  into  a  helix  in  an  upward  direction  away  from  the 
lower  plate.  The  difference  of  potential  between  the  plates  was  measured 
by  a  Kelvin  multicellular  voltmeter. 

The  discharge  chamber  with  its  electrostatic  plates  was  surrounded 
by  a  uniform  magnetic  field,  furnished  by  two  large  coils  MI  and  Af2, 
each  41  cm.  in  diameter  and  30  cm.  high.  By  means  of  proper  supports, 


3IO  J.  B.  NATHANSON.  [§S?5! 

they  were  separated  from  each  other  by  a  distance  of  8.5  cm.  This 
admitted  the  introduction  of  the  Wehnelt  cathode  C  into  the  discharge 
chamber,  and  at  the  same  time  allowed  observations  to  be  taken  on  the 
helix  through  the  plate  glass  window. 

A  Grassot  flux-meter  was  employed  to  determine  the  magnetic  inten- 
sity H  for  any  given  value  of  the  current  J,  through  the  coils.  The  dis- 
charge chamber  was  removed  from  within  the  coils,  and  the  small  test 
coil  of  the  flux-meter  was  properly  supported  in  the  region  occupied  by 
the  helix.  Flux-meter  readings  were  plotted  against  the  values  of  J  in 
amperes,  giving  a  straight  line  curve  through  the  origin.  From  the 
tangent  of  the  curve,  and  the  dimensions  of  the  test  coil,  the  following 
relation  was  found  between  H  and  /,  where  H  is  in  gausses,  and  I  is  in 
amperes, 

H  =  57098/. 

The  maximum  diameter  of  the  cathode  ray  circle  employed  in  this 
investigation  was  about  12  cm.  To  test  the  constancy  of  the  magnetic 
field  over  this  area,  the  small  test  coil  was  moved  outwards  from  the 
axis  of  the  magnetic  coils,  noting  the  flux-meter  readings  for  various 
distances  of  the  test  coil  from  the  axis,  the  current  through  the  magnetic 
coils  being  kept  constant.  It  was  found  that  the  flux-meter  deflections 
were  practically  constant  over  a  region  of  16  cm.  diameter.  This  there- 
fore insured  a  constant  field  over  the  region  traversed  by  the  rays. 

Since  the  beam  of  cathode  rays  issuing  from  the  small  lime  speck  on  the 
Wehnelt  cathode  is  so  compact  and  well  defined,  the  usual  encumbrances 
of  diaphragms,  so  necessary  in  the  case  of  ordinary  cold  cathodes,  were 
done  away  with,  and  the  Wehnelt  cathode  was  introduced  right  into  the 
electrostatic  field  through  a  hole  in  the  side  of  the  discharge  chamber. 
The  manner  of  mounting  the  Pt  strip  on  which  the  lime  speck  was  de- 
posited, was  that  employed  recently  by  Knipp.1  The  ground  glass  joint 
permitted  the  rotation  of  the  cathode  about  an  axis  perpendicular  to  the 
lines  of  magnetic  force.  The  cathode  beam  could  thus  be  oriented  around 
till  its  path  was  perpendicular  to  the  lines  of  magnetic  force.  This 
arrangement  therefore  admitted  of  easy  adjustment  for  the  obtaining 
of  the  beam  in  the  form  of  a  perfect  circle. 

The  small  lime  surface  was  obtained  by  the  placing  of  a  minute  particle 
of  Bank  of  England  sealing  wax  on  the  Pt  strip  and  then  electrically 
heating  the  strip  slowly  up  to  redness.  The  sealing  wax  was  thereby 
changed  into  a  small  round  white  speck  of  lime  whose  diameter  varied 
from  0.5  to  I  mm. 

The  discharge  potential  employed  was  1,000  volts  and  was  furnished 

1  PHYS.  REV.,  p.  58,  January,  1912. 


DETERMINATION  OF  e/m  AND  v.  31  I 

by  a  large  set  of  small  storage  cells.  The  cathode  was  grounded  and  con- 
nected to  the  (  — )  pole  of  the  battery.  The  (+)  pole  was  connected 
through  a  water  resistance  to  the  anode  which  was  in  the  form  of  an  Al 
collar  on  the  inside  of  the  tube  T2. 

METHOD  OF  PROCEDURE. 

The  Wehnelt  cathode  rays  are  easily  absorbed  by  any  residual  gas  in 
the  tube  and  hence  are  obtainable  with  distinctness  only  at  a  very  high 
vacuum.  The  vacuum  used  was  therefore  the  highest  obtainable  by 
means  of  a  Gaede  pump  and  charcoal  cooled  to  liquid  air  temperature. 

The  cathode  beam  was  started  by  closing  the  i,ooo-volt  discharge 
circuit,  and  then  slowly  heating  the  Pt  cathode  to  redness.  It  usually 
took  some  time  for  the  cathode  beam  to  appear,  the  first  appearance  of 
the  beam  being  in  the  form  of  a  whitish  flaky  cloud.  The  temperature 
of  the  Pt  was  then  slowly  increased  till  the  flaky  cloud  changed  into  a 
sharp  beam  which  issued  normally  from  the  cathode.  This  beam  was 
usually  not  perpendicular  to  the  lines  of  magnetic  force  and  hence  when 
the  magnetic  field  was  applied  the  beam  changed  into  a  helix.  By 
rotating  the  cathode  in  the  ground  glass  joint,  this  helix  was  readily 
changed  into  a  perfect  circle  which  lay  in  a  horizontal  plane. 

The  telescope  of  the  cathetometer  was  then  sighted  on  the  plane  of 
the  circle,  the  horizontal  cross  wire  being  placed  on  the  horizontal  edge 
of  the  circle  at  a,  Fig.  2.     Upon  application  of  the 
electrostatic  field,  the  circle  was  drawn  out  into  a  *%^% 

helix  whose  diameter  was  usually  somewhat  less  *^> 

than  the  diameter  of  the  circle.     The   horizontal    b_<— "'' 
cross  wire  of  the  telescope  was  then  sighted  at  b     a 
to  obtain  the  electrostatic  deflection  for  1/2  turn, 
the  difference  in  the  cathetometer  readings  between  Fig  2. 

b  and  a  giving  the  amount  of  this  deflection. 

The  diameter  of  the  circle  was  measured  by  placing  the  leg  of  a  square 
against  the  plate  glass  window,  and  moving  the  square  along  till  the  edge 
of  the  circle  at  one  half  turn  was  in  line  with  the  other  leg  of  the  square. 
The  same  was  done  for  the  other  side  of  the  circle  at  the  cathode.  The 
difference  between  the  two  positions  gave  the  diameter  to  within  I  per 
cent.,  as  close  a  measurement  as  could  be  warranted  by  the  slight  fuzziness 
of  the  boundary  of  the  beam. 

It  was  found  that  the  lime  would  continually  deteriorate  and  fall  off 
from  the  hot  Pt  so  that  the  beam  would  weaken  and  fade  away  with 
continual  use.  This  necessitated  the  raising  of  the  temperature  of  the  Pt 
to  bring  the  beam  back  again  to  distinctness.  Thus  during  the  course  of 


312 


J.  B.  NATHANSON. 


[SECOND 

[SERIES. 


an  experiment,  the  temperature  of  the  Pt  was  intermittently  raised  from 
red  to  white  heat. 

DISCUSSION. 

The  values  of  e/m  vary  from  1.27  to  2.07  X  io7,  giving  an  average  value 
of  1.61  X  io7.  This  agrees  favorably  with  Wehnelt's  value  of  1.48  and 
Knipp's  value  of  1.5,  but  is  less  than  Classen's  value  of  1.773  obtained  by 
a  photographic  method.  The  values  of  v  vary  from  i.oo  to  1.75  X  io9 
cm.  per  second,  giving  an  average  value  of  1.39  X  io9.  We  would  of 
course  expect  v  to  vary  with  the  different  temperatures  employed. 

It  might  be  instructive  to  check  this  value  of  v  by  another  method. 
If  V  is  the  potential  difference  between  anode  and  cathode,  then  we  have 
from  the  equivalence  of  electrical  and  kinetic  energy, 


V  =  ^    2—  V. 

\     m 

Supplying  in  this  equation  V  =  1,000  volts,  and  e/m  =  1.61  X  io7,  v  is 
found  to  be  1.79  X  io9  cm.  per  second.  This  is  somewhat  higher,  but 
of  the  same  order,  than  the  value  of  v  experimentally  obtained.  However 
the  actual  difference  of  potential  between  anode  and  cathode  had  it  been 
carefully  examined,  by  means  of  a  sounder,  would  have  been  found  less 
than  1,000  volts. 

TABLE  I. 

Distance  between  the  electrostatic  plates  =  6.60  cm. 


Amperes, 

Gausses, 
H. 

Volts, 
V. 

Cm., 

z. 

Cm.,  3 
zr. 

elm  X  io-7. 

v  X  io-9. 

1 

3.30 

18.84 

81.3 

1.01 

10.1 

1.71 

1.62 

2 

3.99 

22.78 

81.2 

0.85 

7.7 

1.39 

.21 

3 

3.33 

19.01 

79.5 

1.08 

10.0 

.56 

.14 

4 

4.70 

26.84 

119.5 

0.98 

6.4 

.27 

.09 

5 

3.20 

18.27 

80.0 

1.10 

10.0 

.64 

.49 

6 

3.75 

21.41 

119.3 

1.33 

7.7 

.46 

.20 

7 

3.43 

19.58 

79.5 

0.99 

9.3 

.59 

.44 

8 

2.90 

16.56 

120.0 

1.94 

10.2 

.70 

.43 

9 

3.62 

20.67 

83.0 

1.01 

8.1 

1.44 

.20 

10 

2.90 

16.56 

120.0 

1.72 

10.3 

1.91 

.63 

11 

3.61 

20.61 

126.0 

1.30 

8.7 

1.71 

.53 

12 

3.35 

19.13 

43.0 

0.43 

8.9 

2.07 

1.75 

13 

4.20 

23.98 

120.0 

1.05 

7.2 

1.49 

1.29 

Mean . 


1.61 


1.39 


Returning  to  the  values  of  e/m  given  in  Table  I.,  we  notice  that  they 
vary  somewhat  among  themselves.  It  seems  that  Wehnelt1  had  the 
same  experience,  for  his  table  shows  e/m  to  vary  from  1.34  to  1.8 1  X  io7. 

1  Ann.  d.  Phys  ,  14,  p.  425,  1904. 


]  DETERMINATION  OF  e/m  AND  v.  313 

Since  the  method  of  this  investigation  is  so  different  from  Wehnelt's 
method,  there  seems  to  be  no  other  conclusion  than  that  the  cause  of 
the  variation  of  e/m  lies  in  the  nature  of  the  Wehnelt  cathode  itself.  It 
was  previously  mentioned  that  the  lime  was  continually  disappearing 
from  the  hot  Pt  necessitating  now  and  then  the  raising  of  the  temperature 
of  the  Pt  to  obtain  a  sharper  beam.  Other  recent  work  in  this  laboratory 
on  the  Wehnelt  cathode  shows  quite  conclusively  that  the  activity  of  the 
hot  lime,  when  supplied  by  Bank  of  England  sealing  wax,  falls  off  rapidly 
with  use — the  current  rising  to  successively  lower  and  lower  maxima 
each  succeeding  day  when  heated  to  the  same  temperature.  It  is 
evident,  due  to  the  sputtering  of  the  hot  lime  cathode  together  with  the 
probable  complex  character  of  the  lime  obtained  from  the  sealing  wax, 
that  the  source  of  the  negative  carriers  of  electricity  is  not  a  constant  one. 
Slight  variations  in  the  heating  current  made  correspondingly  very  large 
variations  in  the  density  of  the  cathode  beam.  This  inconstancy  must 
account  in  a  large  measure  for  the  variation  of  e/m. 

The  disturbing  effect  of  introducing  the  cathode  between  the  electro- 
static field  plates  was  less  than  the  error  due  to  the  variations  just  men- 
tioned. This  was  shown  to  be  the  case  by  introducing  the  hot  Pt  strip 
carrying  the  lime  up  through  a  slot  in  the  lower  plate  and  adjusting  so 
that  the  cathode  beam,  when  bent  into  a  circle  by  the  strong  magnetic 
field,  just  grazed  the  upper  surface  of  this  plate,  the  electrostatic  field 
being  zero. 

In  addition  it  might  be  said  that,  apart  from  all  quantitative  measure- 
ments, the  helical  method  is  most  beautiful  in  its  nature,  and  the  appa- 
ratus serves  very  excellently  as  a  demonstration  piece  for  the  magnetic 
and  electrostatic  deflection  of  cathode  rays. 

In  conclusion  I  take  this  opportunity  of  expressing  my  thanks  to  Pro- 
fessor A.  P.  Carman  for  the  facilities  that  were  so  kindly  placed  at  my 
disposal,  and  to  Dr.  C.  T.  Knipp  who  made  this  work  possible  by  his 
kind  help  and  suggestions. 

LABORATORY  OF  PHYSICS, 
UNIVERSITY  OF  ILLINOIS, 
June,  1913. 


[Reprinted  from  the  AMERICAN  JOURNAL  OF  SCIENCE,  Vol.  xxxvi,  Decem- 
ber, 1913.] 


ART.  LI. —  On  the   Use  of  Sealing  Wax  as  a  Source  of  Lime 
for  the  Wehnelt  Cathode ;  by  NELLIE  !N.  HORNOR. 

IN  the  Wehnelt*  cathode  as  first  employed  various  metallic 
oxides  were  used  as  salts.  Those  of  calcium,  barium,  and 
strontium  gave  an  abnormally  large  discharge  of  negative  elec- 
tricity. The  sign  of  the  electrification  depends  upon  the  metal 
used  and  also  upon  the  class  of  the  salt.f  Willows  and  Picton;): 
used  nickel  and  platinum  strips  for  the  cathode,  while  Richard- 
son §  employed  both  the  tube  and  strip  methods,  and  recently 
Sheard  ||  used  the  tube  method. 

The  conditions  affecting  the  efficiency  of  this  form  of  cathode 
have  also  been  studied  by  Horton,!"  Garrett,**  and  Wilson.ff 
In  the  work  by  Willows  and  Picton,  referred  to  above,  they 
found  that  when  using  a  pressure  of  -002mm  Hg  and  up,  a  volt- 
age of  36,  and  a  temperature  of  1100  degrees  Centigrade,  there 
was  a  decided  increase  in  the  activity  of  the  salt  when  the 
cathode  had  stood  cold  over  a  period  of  several  days  or  weeks. 
They  also  found  a  greatly  increased  stream  of  electrons  on 
making  the  discharge  after  it  had  been  broken  for  a  time,  the 
heating  current  continued  the  while.  The  accumulation  of 
electrons  in  the  heated  lime  was  dependent  upon  the  interval 
of  time. 

It  has  been  known  for  some  time  that  ordinary  sealing  wax 
makes  a  fairly  good  source'  of  lime.  The  Bank  of  England 
wax  seems  quite  satisfactory.  Its  use,  however,  was  until 
recently  confined  to  the  Cavendish  laboratory.  For  some  time 
it  has  been  evident  that  its  behavior  as  a  lime  is  different  than 
that  of  the  oxides  which  are  generally  used.  Hence  the  fol- 
lowing investigation,  in  which  the  object  is  a  study  of  the 
activity  of  this  source  of  lime  together  with  the  various  con- 
ditions best  suited  for  its  efficient  working. 

Description  of  Apparatus. 

A  sketch  of  the  apparatus  used  is  shown  in  fig.  1.  M.N  is  a 
two  liter  spherical  flask,  S'  is  a  drying  bulb,  B'  the  heating 
circuit,  C  the  cathode,  and  A  the  anode.  The  aluminium  disc 
G'  was  connected  through  a  reversing  switch  K1  to  the  galvano- 

*Phil.  Mag.,  vol.  x,  July,  1905. 

t  J.  J.  Thomson,  Proc.  Camb.  Phil.  Soc.,  vol.  xiv,  1906. 

tPhys.  Soc.,  London,  Proc.,  June,  1911. 

§Phil.  Mag.,  vol.  xx,  1910. 

||  Phil.  Mag.,  vol.  xxv,  March,  1913. 

If  Phil.  Trans.  Sec.  A,  vol.  ccvii,  1907. 

**  Phil.  Mag.,  vol.  xx.  October,  1910. 

ft  Phil.  Mag.,  vol.  xxi,  May,  1911. 


592        Hornor —  Use  of  Sealing  Wax  as  a  Source  of 

meter  and  to  earth.  A  high  potential  cabinet  T  furnished  the 
voltage,  the  positive  terminal  was  connected  through  a  water 
resistance  to  earth  and  to  the  anode  and  the  negative  through 


FIG.  1. 


0  40  60 

Time   in 


120 


160 


2-40 


280 


a  switch  K  to  the  cathode.  A  voltmeter,  YM.  and  an  induc- 
tion coil,  #,  were  connected  to  the  switch  K  as  shown.  1,  2, 
3,  4,  and  £  are  red  wax  joints.  The  method  of  mounting  the 
cathode  was  that  recently  described  by  Knipp.*  A  K alder 
D'Arsonval  galvanometer,  67,  of  a  fair  degree  of  sensitiveness 
was  employed. 

*Phys.  Rev.,  vol.  xxxiv,  March,  1912. 


Lime  for  the  Wehnelt  Cathode. 


593 


Method. 

The  electrons  fell  upon  the  disc  6r',  located  opposite  and 
about  4mm  from  the  cathode,  and  the  resulting  current  was 
indicated  by  the  galvanometer.  With  each  galvanometer 
reading,  which  was  the  mean  of  two  deflections,  the  pressure, 


FIG.  3. 


0          30          60         90          120 

Time  in  minutes 


180        210         240        270 


discharge  voltage,  and  heating  current  readings  were  taken. 
The  heating  current  was  kept  strictly  constant.  The  pressure 
was  also  kept  practically  constant  by  occasional  pumping. 

After  mounting  the  platinum  strip,  a  very  small  piece  of  the 
red  wax  was  placed  centrally  upon  it.  The  wires  D  and  E* 
were  then  connected  to  the  heating  circuit  and  the  current  was 


594:        Hornor—  Use  of  Sealing  Wax  as  a  Source  of 

FIG.  4. 


3.0 
2.7 


T     2-l 

X1'8 

0-l.S 

£ 

tt.    1.2 

•S    .9 


0  20  40 

T\  me  \n  \nour3 


60 


80 


FIG.  5. 


w 

1.2 
1.0 

B 
ij- 

0 

x  .6 

G. 

i* 

*— 

c 

£^ 

3 

O 

0 

\ 

\ 

\ 

\ 

\ 

\ 

A 

?» 

\ 

^ 

\ 

^ 

=N>. 

»~0 

0- 

o-o 

t—  0- 

0         20         40         60         80         100        120         140 

Time   in  mmute5 


.Lime for  the  Wehnelt  Cathode. 


595 


gradually  increased  until  the  disc  of  lime  became  white.  The 
lime  was  thus  deposited  on  the  platinum  strip.  The  tube  was 
then  placed  in  position,  sealed,  and  the  apparatus  evacuated 
until  the  pressure  was  -OlS"1111  of  mercury  or  less.  Pressures 
ranging  from  '003  to  -Q4:mm  were  used.  The  apparatus  was 
usually  allowed  to  stand  over  night  after  evacuating  to  allow 
the  P2O6  to  absorb  the  moisture. 

The  heating  current  was  adjusted  until  the  temperature  of 
the  platinum  was  that    corresponding  to  a  light  cherry -red. 

FIG.  6. 


r4 


^  2 


00 


^~~ 

^-o 

=3 

=3 

=0 

^••H 

—  ff 

-^>- 

BOK= 

=CF= 

—^^ 

=Sr- 

s' 

"" 

/ 

^ 

? 

0          40          80          120          160         200         MO        fl 

JO           J20          360          400. 

Discharge   in  \Jolts 


Since  it  was  necessary  to  renew  the  lime  frequently,  a  reliable 
thermo-junction  connection  was  nearly  impossible  and  hence 
no  attempt  was  made  to  determine  the  temperature.  It  was, 
however,  kept  strictly  constant  during  any  given  run  or  set  of 
runs.  The  discharge  circuit  was  closed,  the  time  noted,  and 
the  galvanometer  watched  for  the  current  to  start.  When  a 
cathode  with  fresh  lime  was  heated  the  first  time  the  discharge 
did  not  start  immediately  but  only  after  from  ten  to  thirty 
minutes  if  conditions  were  favorable.  An  induction  coil  may 
be  used  to  start  the  discharge,  but  this  complicates  matters  as 
there  seems  to  be  a  gradual  rise  due  to  the  ionization  caused  by 
the  induction  coil  discharge.  The  cathode  stream  may  also  be 
started  more  quickly  by  making  the  heating  current  larger  for 
a  short  time;  however  if  this  is  done  the  increase  to  a  maximum 
and  the  maximum  itself  are  not  shown,  —  only  the  part  of  the 
curve  due  to  the  decay  is  obtained. 


Discussion  of  Curves. 

The  effect  of  changes  in  the  heating  current  is  shown  by 
curve  1,  fig.  2.  A  very  small  change  in  this  current,  in  fact 
one  which  the  eye  could  scarcely  detect  on  the  ammeter 
where  two  scale  divisions  read  1/10  of  an  ampere,  produced 
quite  an  appreciable  effect  upon  the  galvanometer  deflections. 


596        Hornor —  Use  of  Sealing  Wax  as  a  Source  of 

After  two  hours  the  heating  current  became  fairly  steady  and 
a  smooth  curve,  from  A  to  B,  was  obtained.  The  cathode  was 
allowed  to  stand  cold  with  the  vacuum  up  for  two  days.  On 
heating  to  the  same  temperature  and  starting  the  discharge 
again  the  current  rose  to  a  maximum  value  in  an  hour  and  then 
remained  comparatively  steady  for  the  rest  of  the  run.  The 
steady  current  value  shown  in  curve  2,  fig.  2,  was  very  little 
smaller  than  the  maximum,  which  in  turn  was  much  smaller 
than  the  steady  value  for  the  preceding  run.  After  five  days 
another  run  was  made  with  the  same  platinum  strip  and  lime 
heated  to  the  same  temperature.  This  run  gave  a  maximum 
less  than  the  steady  value  for  the  second  run,  as  shown  by 
curve  3.  It  has  the  same  general  characteristics  as  curve  2. 
The  discharge  voltage  for  these  curves  was  approximately  400 
volts,  the  heating  current  4'63  amperes,  and  the  pressure  varied 
from  -005  to  -016mrn  Hg.  In  the  last  two  curves  the  heating 
current  was  steady.  The  curves  in  fig.  2  indicate  that  the 
activity  of  the  red  wax  decays  with  time.  This  is  also  shown 
in  a  striking  manner  by  curves  1,  2,  and  3,  fig.  3.  The  maxi- 
mum value  of  the  current  during  any  given  run,  after  the  lime 
had  been  cold  from  1  to  4  days,  was  always  less  than  the  steady 
value  of  the  current  for  the  preceding  run.  Apparently  when 
the  lime  is  allowed  to  become  cold  it  is  not  able  to  regain  the 
activity  it  had  at  the  end  of  the  previous  run.  However,  the 
activity  that  it  does  acquire  it  regains  quickly. 

The  relation  between  the  maxima  and  the  number  of  hours 
between  them  is  shown  by  fig.  4.  Evidently  these  maxima 
decrease  very  rapidly  at  first. 

When  the  lime  is  used  for  the  first  time  it  is  very  difficult  .to 
adjust  the  heating  current  to  a  value  that  will  give  smooth  curves 
similar  to  2  and  3  in  fig.  2.  The  form  of  the  curve  is  more 
likely  to  be  that  shown  in  curve  1,  fig.  3.  In  this  the  number 
of  electrons  emitted  for  the  first  two  and  one-half  hours  in- 
creased very  slowly,  when  suddenly  it  rose  to  a  very  high  max- 
imum and  then  almost  as  suddenly  fell  to  a  much  lower  steady 
value.  The  temperature  was  that  corresponding  to  cherry-red. 
This  sudden  and  very  high  maximum  indicates  that  most  of 
the  electrons  which  may  possibly  be  emitted  under  these  con- 
ditions acquired  sufficient  energy  to  escape  almost  simultane- 
ously and  thus  caused,  as  it  were,  an  explosion.  Curves  2  and 
3,  in  fig.  3,  again  show  the  same  characteristics  as  curves  2 
and  3  in  fig.  2.  After  the  lime  has  once  been  heated,  the  sub- 
sequent currents  start  much  more  easily  and  rise  to  a  maximum 
more  quickly,  suggesting  that  the  electrons  are  in  a  state  more 
favorable  to  emission.  The  beam  was  visible  to  the  eye  in 
curves  1,  2,  and  3,  fig.  3,  from  A,  B,  and  6yon. 

If  the  discharge  voltage  was  cut  off  while  the  heating  con- 


Lime  for  the  Wehnelt  Cathode.  597 

tinned,  the  current  obtained  on  again  closing  the  discharge 
circuit  was  in  every  case  smaller  than  it  was  just  before  breaK- 
ing.  This  is  shown  by  fig.  5.  The  behavior  of  the  lime  seemed 
to  be  much  the  same  as  though  it  had  been  allowed  to  stand  in 
the  cold,  except  that  the  effect  was  not  so  pronounced.  This 
shows  that  the  decrease  in  activity  for  short  intervals  of  no  dis- 
charge was  slight,  yet  definite,  if  the  lime  was  kept  hot.  This 
result  does  not  agree  with  that  of  Willows  and  Picton,  who 
observed,  for  the  salts  that  they  used,  a  decided  increase  in 
activity  under  the  same  conditions. 

Data  on  the  saturation  voltage  were  obtained  as  follows  :  for 
a  given  heating  current  and  a  discharge  voltage  of  40  volts 
the  run  was  continued  until  the  current  became  steady,  after 
which  the  voltage  was  advanced  by  steps  of  40  volts  at  inter- 
vals of  10  minutes,  the  maximum  current  being  recorded  each 
time.  The  curve  in  fig.  6  shows  the  results  obtained.  There 
was  saturation  at  200  volts. 

The  Bank  of  England  wax  upon  analysis  was  found  to  have 
the  following  principal  constituents  :  calcium  sulphate  (gyp- 
sum), barium  sulphate  (heavy  spar),  mercuric  sulphide  (cinna- 
bar), and  shellac. 

Summary. 

It  was  shown  that  when  Bank  of  England  sealing  wax  is  used 
as  the  source  of  lime  there  is  a  falling  off  in  the  activity 
with  time. 

When  a  maximum  is  reached  most  of  the  electrons  are 
emitted  during  the  first  run. 

When  the  discharge  is  broken  while  the  heating  current  is 
maintained  there  is  a  slight  falling  off  in  the  negative  stream. 

The  above  results  are  exactly  opposite  to  those  obtained  by 
Willows  and  Picton  using  calcium  oxide  on  a  platinum  strip, 
while  they  agree  in  part  with  the  observations  of  Sheard,  who 
found  that  the  activity  for  cadmium  iodide  and  iodine,  with 
the  tube  method,  decreased  during  any  given  run. 

The  saturation  voltage  was  found  to  be  200  volts. 

There  was  a  falling  off  in  the  maxima  for  successive  runs, 
and  the  steady  current  for  any  given  run  was  usually  much 
smaller  than  that  for  the  preceding  run  with  the  same  lime. 

In  conclusion,  the  writer  takes  pleasure  in  thanking  Profes- 
sor A.  P.  Carman  for  the  facilities  of  the  department,  and  Dr. 
C.  T.  Knipp  for  suggesting  the  problem  and  assistance  in  car- 
rying out  the  details  of  this  investigation. 

Physical  Laboratory, 

University  of  Illinois. 


Acoustical   Effect  of  Fireproofed 
Cotton-Flannel  Sound  Absorbers 


Reprinted  from  Engineering  News 
January  29,  1914 


BY   P.  R.  WATSON! 

Cotton-flannel  was  found  to  be  a  fairly  good  absorber 
of  sound,  during  a  recent  investigation  of  the  acoustic 
properties  of  the  Auditorium  at  the  University  of  Illi- 
nois. It  is  easy  to  obtain  and  to  install;  it  is  also  com- 
paratively cheap;  but,  unfortunately,  it  is  inflammable 
The  question  then  arose  as  to  the  effect  of  fireproofing 
upon  the  sound-absorbing  qualities  of  cotton-flannel. 

A  search  through  the  literature  on  the  subject  did  not 
yield  very  much,  and  apparently  little  has  been  done  on 
this  particular  phase  of  the  problem.  In  1902,  Norton1 
published  an  account  of  some  experimental  tests  of  the 
sound-absorbing  qualities  of  materials  that  were  already 
fireproof.  Sabine2  describes  some  experiments  in  which 
hair  felt  was  covered  by  burlap  attached  by  silicate  of 
soda.  In  neither  of  these  investigations  was  it  apparent 
just  what  effect  the  process  of  fireproofing  had.  The 
author  then  took  up  the  problem  of  testing  flannel  before 
and  after  fireproofing. 

The  observations  were  taken  by  Sabine's  method.3  In 
a  room,  about  20x20  ft.,  cleared  of  all  furniture,  an  organ 
pipe  was  sounded  for  several  seconds  and  then  stopped. 
The  time  taken  for  the  sound  to  die  out  was  noted  by  an 
observer  who  made  the  record  electrically  on  a  chrono- 
graph drum.  This  observation  was  repeated  at  least  ten 
times.  A  similar  set  of  measurements  was  then,  taken 
when  a  large  sheet  of  outing  flannel  was  hung  in  front 
of  one  of  the  walls.  A  third  set  was  taken  with  a  sheet 
of  fireproof ed  cotton-flannel  in  place  of  the  unfireproofed. 

A  summary  of  results  follows;  each  record  is  the  aver- 
age of  at  least  ten  measurements. 

Cotton-flannel 
EmDtv 
Date 

June  26 

June  30 

Average 3.26  2.25*  2.30 


''-The  permanent  fireproofing  of  fabrics  was  briefly  de- 
scribed in  a  news  note  in  "Engineering  News,"  of  Oct.  10, 
1912.— Ed. 

fAssistant  Professor  of  Physics,  University  of  Illinois,  TJr- 
bana.  111. 


Empty 
room 

Un- 
fireproofed 

Fire- 
proofed 

sec. 

sec. 

sec. 

3.3 

2.3 

2.4 

2.4 

2.3 

3.2 

2.2 

2.3 

3.3 

2.1 

2.2 

The  results  indicate  that  the  fireproofing,  for  the  con- 
ditions of  the  experiment,  did  not  materially  change  the 
sound-absorbing  properties  of  the  cotton-flannel.  This 
result  was  rather  surprising  since  it  was  expected  that 
the  fireproofed  material  would  be  the  poorer  absorber  of 
sound.  The  two  samples  used  were  cut  from  the  same 
piece  of  goods.  The  unfireproofed  piece  was  fluffy  and 
rather  thick,  while  the  other  piece  in  process  of  fire- 
proofing  was  soaked  in  a  solution,  then  squeezed  flat  by 
being  run  through  a  wringer,  and  finally  dried. 

1 1  seemed  likely  that  the  fireproofed  piece  would  absorb 
sound  less  readily,  since  it  was  now  squeezed  into  a  closer 
texture  and  its  interstices  apparently  more  or  less  filled 
with  the  fireproofing  substance.  The  experiments,  how- 
ever, showed  it  to  have  the  same  effect  as  the  unfire- 
proofed. Each  sample  was  hung  about  four  inches  from 
a  plastered  wall,  and  pleated  in  folds  so  that  each  width 
of  the  flannel  (30  in.)  covered  only  a  foot.  The  total 
area  of  each  piece  when  in  place  for  the  experiment  was 
about  9x12  sq.ft.  The  flannel  cost  about  15c.  per  yard 
including  fireproofing. 


PREPRINTED  FROM 
THE 

ASTROPHYSICAL   JOURNAL 

AN  INTERNATIONAL  REVIEW  OF  SPECTROSCOPY 
AND  ASTRONOMICAL  PHYSICS 


VOLUME  XXXIX  MAY      1914  NUMBER  4 


A  DETERMINATION  OF  THE  SUN'S  TEMPERATURE 

BY  GLENN  A.  SHOOK 

INTRODUCTION 

In  1906  Moissan  carried  out  a  number  of  experiments  upon  the 
vaporization  of  metals.1  He  placed  the  temperature  of  his  furnace 
at  3500°  C.  and  made  the  statement  that  all  known  elements  vola- 
tilize at  that  temperature.  Now  it  is  thought  by  Schulz  that  the 
temperature  of  the  furnace  must  have  been  considerably  above 
3500°  C.  and  probably  as  high  as  the  sun's  photosphere  which  he 
sets  at  5400°  C.2  He  argued  that  owing  to  the  large  current  used 
by  Moissan  there  was  an  enormous  amount  of  energy  which  had 
no  adequate  escape  by  conduction  or  radiation  and  which  therefore 
must  have  raised  the  temperature  of  the  furnace  up  to  the  point 
where  it  was  checked  by  the  melting  and  evaporization  of  the  lime- 
stone of  which  it  was  constructed.  He  moreover  asserts  that  the 
volatilization  of  the  metals  is  not  to  be  regarded  as  complete. 

We  also  find  the  following  remarks  in  regard  to  molybdenum 
and  tungsten: 

Molybdenum. — The  1 50  grams  were  not  fused  by  a  current  of  500  amperes 
and  no  volts.  After  applying  700  amperes  and  no  volts  for  seven  minutes, 

1  Annales  de  chemie  et  de  physique,  8,  151,  1906. 
3  Astrophysical  Journal,  29,  33,  1909. 

277 


278  GLENN  A.  SHOOK 

the  metal  was  fused  but  nothing  evaporated.     After  twenty  minutes  56  grams 
were  distilled. 

Tungsten. — After  applying  500  amperes  and  no  volts  for  5  minutes  the 
metal  was  not  yet  fused.  After  applying  800  amperes  and  no  volts  for 
twenty  minutes,  boiling  commenced  but  only  25  grams  distilled. 

It  thus  appears  that  the  volatilization  is  partly  a  question  of 
time,  and  when  we  remember  that  the  sun's  photosphere  is  probably 
at  a  temperature  of  8000°  C.  or  9000  °  C.  and  that  such  a  temperature 
has  existed  for  years  and  not  minutes,  we  must  conclude  that  all 
elements  in  the  sun  are  necessarily  in  the  gaseous  state. 

The  following  hypothesis  which  has  been  advanced  by  a  num- 
ber of  investigators1  is  confirmed  by  the  present  research. 

In  the  first  place  the  material  of  the  sun  is  " gaseous,"  that  is, 
it  follows  the  extended  law  for  gases. 

Secondly,  the  radiation  that  reaches  us  comes  from  the  reversing 
layer  alone  or  at  least  only  from  the  superficial  layers  of  the  photo- 
sphere. 

Thirdly,  there  is  a  relatively  large  drop  in  the  temperature  at 
the  reversing  layer. 

If  there  is  considerable  scattering  of  light  due  to  the  gases  of 
the  reversing  layer,  then  the  light  that  reaches  us  comes  only  from 
a  small  depth.  Moreover,  the  scattering  is  greater  for  blue  light 
than  for  red,  consequently  the  blue  part  of  the  spectrum  must  be 
relatively  weaker  than  the  red  part.  Hence,  if  the  temperature 
falls  off  rapidly  as  we  move  outward  radially  through  the  reversing 
layer  we  should  expect  the  temperature  for  blue  light  to  be  less 
than  that  determined  for  red  light.  Also  as  we  move  across  the 
sun's  disk,  we  should  expect  the  apparent  temperature  to  fall  off 
rapidly  as  we  approach  the  limb  and  we  should,  moreover,  expect 
the  temperature  gradient  for  blue  to  be  greater  than  that  for  red. 
This  is  precisely  what  the  writer  finds.  The  sharp  boundary  of 
the  photosphere  is  additional  proof  of  the  gaseous  scattering. 

That  the  scattering  prevents  us  from  seeing  beyond  a  shallow 
depth  of  the  reversing  layer  may  be  shown  by  a  rough  calculation. 

1  Secchi,  Le  soleil,  i,  Book  III,  chap,  iv,  p.  267;  2,  Book  VII,  chap  i,  p.  299; 
Schwarzschild,  "Ueber  das  Gleichgewicht  der  Sonnenatmosphare,"  Gottingen  Nachr., 
Math.  Phys.  Kl.,  1906,  pp.  1-13;  Abbot,  The  Sun,  p.  236. 


THE  SUN'S  TEMPERATURE  279 

The  law  of  molecular  absorption  is  expressed  by  the  following 
formula : 


or 

log^  --  kh 
*« 

where  70=  the  intensity  of  light  incident  upon  the  absorbing 
medium;  7=the  intensity  of  the  transmitted  light;  &  =  the 
fraction  of  light  absorbed  by  unit  thickness  of  the  medium;  and 
h  =  the  thickness  or  height  of  the  absorbing  layer. 

Using  Abbot's1  values  for  the  transmission  of  the  atmosphere 
above  Mount  Wilson  we  have: 

Wave-length  in/u.  ...........  0.4        0.5        0.6        0.7 

Percentage  of  transmission.  ...  76          89          95          97 

Taking  the  Mount  Wilson  atmosphere,  which  is  about  10  miles, 
as  our  unit  thickness,  the  length  of  a  column  of  gas  for  an  extinction 
of  99  per  cent  or  a  transmission  of  i  per  cent  for  a  wave-length  of 
o  .  4  JLC  becomes 

log  o  .  01 
—  -  =—  0.24/2 

0.4343 

or 

h  =  iS.S, 

that  is,  the  column  would  have  to  be  185  miles  if  the  gas  had  the 
same  density  as  the  Mount  Wilson  atmosphere. 

The  relative  densities  of  the  photosphere  and  the  Mount  Wilson 
atmosphere  may  be  determined  by  means  of  Boyle's  Law  as  follows: 

Let  the  pressure,  volume,  and  absolute  temperature  of  the 
former  be  p',  v',  and  T',  and  the  corresponding  quantities  for  the 
latter  be  p,  v,  and  T.  We  may  now  write: 

pv=RT 
and 


hence 

pv  _T 
pV~Tf 

1  Nature,  81,  97,  1909. 


280  GLENN  A.  SHOOK 

Assuming  that  the  pressure  of  the  reversing  layer  is  about  5  atmos- 
pheres, that  its  mean  temperature  is  7000°  A.,  and  that  the 
temperature  of  the  earth's  atmosphere  is  250°  A.,  we  obtain  the 
relation  : 

_  250 


5X?/    7000* 

Writing  ds  for  the  density  of  the  reversing  layer  and  de  for  the 
density  of  the  earth's  atmosphere,  the  above  equation  becomes: 

^250X5 
de      7000 

Hence  a  column  of  gas  on  the  sun  sufficient  to  produce  an  extinction 
of  99  per  cent  at  wave-length  o  .  4  JJL  would  have  to  be 

i8.5XioX-^—  —  r-=iooo  miles  high. 

In  this  manner  Table  I  was  constructed 

TABLE  I 

Wave-Length  Miles 

0.4  /A  ...................................  IOOO 

0.5  ....................................  2400 

0.6  ....................................  5200 

0.7  ....................................  8600 

Since  the  radius  of  the  sun  is  435,000  miles,  it  is  readily  seen 
that  the  radiation  which  we  are  utilizing  for  the  estimation  of 
temperature  comes  from  only  the  outermost  solar  layers.  It  is 
also  observed  that  for  short  wave-lengths  the  depth  to  which  we 
are  able  to  penetrate  is  smaller  than  that  which  obtains  for  the 
longer  wave-lengths. 

EXPERIMENTAL   METHOD   FOR   THE   DIRECT  DETERMINATION   OF   THE 
SUN'S   APPARENT   TEMPERATURE 

The  method  employed  by  the  writer  for  the  determination  of 
the  sun's  apparent  temperature  is  an  application  of  Planck's 
formula  for  the  visible  spectrum.  In  this  method  the  brightness 
of  the  sun's  disk  is  compared  photometrically  with  the  brightness 
of  the  filament  of  a  miniature  incandescent  lamp  for  three  different 
colors.  To  carry  out  these  observations  the  Department  of 


THE  SUN'S  TEMPERATURE  281 

Astronomy  of  this  university  kindly  permitted  the  use  of  their 
small  observatory,  which  is  equipped  with  a  six-inch  equatorial 
telescope.  A  new  eyepiece  was  constructed,  providing  a  receptacle 
for  the  lamp  between  the  eye-lens  and  the  field-lens.  A  new  finder, 
provided  with  a  micrometer  scale  and  parallel  hairs,  was  also 
attached  to  the  telescope. 

An  image  of  the  sun  is  formed  by  the  objective  in  the  focal 
plane  of  the  eyepiece.  The  .incandescent  lamp  is  adjusted  until 
its  filament  lies  in  the  plane  of  the  image  of  the  sun's  disk. 

If  one  looks  through  the  telescope  when  it  is  directed  toward  the 
sun  he  sees  the  image  of  the  lamp-filament  superimposed  upon  the 
image  of  the  sun's  disk.  Now  by  varying  the  current  through  the 
lamp  the  filament  can  be  made  to  disappear  against  the  bright 
background  of  the  sun's  image.  When  this  condition  obtains,  the 
temperature  of  the  filament  is  equal  to  the  apparent  black-body 
temperature  of  the  image,  and  by  means  of  Planck's  formula  the 
apparent  black-body  temperature  of  the  sun's  disk  can  be  esti- 
mated if  the  temperature  of  the  filament  is  known  as  a  function  of 
the  current  through  the  lamp. 

In  the  present  investigation  the  lamps  used  were  calibrated 
by  the  Bureau  of  Standards.  The  eyepiece  that  was  used  in  the 
equatorial  and  which  contained  a  lamp  receptacle  was  fitted  into 
a  small  telescope  and  this  arrangement  was  used  by  the  bureau  in 
calibrating  the  lamps  by  means  of  their  standard  black  body. 
They  furnished  for  each  lamp  a  table  containing  a  series  of  temper- 
atures and  the  corresponding  currents  through  the  lamp.  The  error 
which  might  be  caused  by  reflections  from  the  lamp  globe  and  eye- 
piece lenses  was  thus  eliminated. 

As  a  matter  of  fact,  the  entire  filament  will  never  disappear 
since  all  parts  are  not  of  the  same  intensity,  but  one  always  uses 
the  central  portion  of  the  tip  and  this  is  practically  uniform  in 
intensity. 

The  filament  (Fig.  2)  may  be  moved  about  easily  to  any  point 
on  the  disk,  which  is  represented  by  the  dotted  line,  by  means  of 
the  right  ascension  and  the  declination  screws.  Fig.  i  shows  the 
reticle  of  the  finder  with  the  scale  and  parallel  spider  lines.  These 
parallel  lines  are  adjusted  so  that  their  distance  apart  is  equal  to 


282 


GLENN  A.  SHOOK 


the  diameter  of  the  sun's  image,  and  they  are,  moreover,  always 
parallel  to  the  ecliptic. 

The  axis  of  the  lamp  is  generally  maintained  perpendicular  to 
the  ecliptic.  The  lamp  is  connected  in  series  to  a  few  storage  cells, 
an  adjustable  resistance,  and  a  milliammeter  (Fig.  3). 


FIG.  i 


FIG.  2 


This  arrangement  of  lamp  and  eyepiece,  which  is  the  result  of 
some  experimenting,  was  found  to  be  the  most  satisfactory.  With 
an  equatorial  as  small  as  this  one  the  image  is  only  about  i  cm  in 
diameter,  and  in  order  to  investigate  the  intensity  along  any  radius, 
i.e.,  along  a  distance  of  0.5  cm,  with  any  accuracy  it  is  necessary 


ii 


mm- 


FIG.  3 

to  have  a  rather  large  magnification.  In  order  to  obtain  a  clear 
image  the  field-lens  is  also  indispensable.  Again,  with  the  present 
arrangement  the  globe  of  the  lamp  just  about  fills  up  the  space 
between  the  two  lenses  and  therefore  it  is  not  in  focus;  conse- 
quently when  one  looks  at  the  tip  of  the  filament  the  contour  of  the 
globe  is  scarcely  noticed.  If  an  eye-lens  of  longer  focal  length  were 
used,  the  globe  would  cause  a  distortion  of  the  image. 


THE  SUN'S  TEMPERATURE  283 

The  problem  of  diminishing  the  intensity  of  the  sun's  image  to 
that  of  an  incandescent  lamp-filament  presents  no  small  difficulty. 
The  intensity  may  be  partly  diminished  by  diaphragming  down 
the  objective,  but  on^e  cannot  resort  solely  to  this  method  without 
seriously  impairing  the  definition  of  the  image.  When  the  aperture 
is  made  as  small  as  is  permissible,  an  absorption  glass  may  be  used, 
but  it  is  almost  necessary  to  use  three  or  more  if  the  absorption 
coefficient  of  the  arrangement  is  required  in  any  calculation.  The 
density  of  a  single  glass  required  to  make  the  necessary  reduc- 
tion in  intensity  is  so  great  that  it  is  impossible  to  measure  its 
absorption  coefficient  with  any  accuracy.  Since  the  absorption 
of  these  glasses  is  never  absolutely  general,  i.e.,  non-selective, 
and  since  they  differ  slightly  among  themselves,  it  is  necessary 
to  measure  the  absorption  factor  of  each  glass  for  each  wave- 
length used. 

Moreover,  the  optical  properties  of  these  glasses  must  be  almost 
as  good  as  those  of  the  telescope  objective;  otherwise  aberrations 
would  result.  It  is  for  this  reason  that  it  is  practically  impossible 
to  use  a  large  telescope  since  the  absorption  glasses  would  have  to 
be  made  with  as  much  care  as  the  objective  of  the  telescope. 

In  order  to  determine  the  best  arrangement  for  the  six-inch 
equatorial  used  in  this  investigation  a  number  of  observations 
were  carried  out  upon  the  moon's  disk.  The  most  conspicuous 
craters  were  carefully  studied  with  a  full  objective  and  then  with 
a  number  of  diaphragms  having  apertures  of  different  size.  In 
this  manner  it  was  found  that  an  aperture  of  about  i .  5  cm  still 
produced  good  definition.  In  addition  to  this  diminishing  of  the 
aperture  three  absorption  glasses  were  also  used.  The  objective 
of  the  finder  was  also  stopped  down  and  in  addition  an  absorption 
glass  was  used. 

Monochromatic  light  was  produced  by  placing  colored  glasses 
directly  before  the  eye- lens  R  (Fig.  3).  It  is  practically  impossible 
to  obtain  a  single  colored  glass  which  is  even  approximately  mono- 
chromatic. Four  colors  of  Jena  glass  were  obtained  from  Petitdi- 
dier,  Chicago — namely,  red,  yellow,  green,  and  blue.  The  red  is 
remarkably  good,  transmitting  only  a  red  band,  and  that  rather 
narrow.  The  yellow,  which  appeared  monochromatic  to  the 


284  GLENN  A.  SHOOK 

unaided  eye,  was  found  to  transmit  almost  the  entire  spectrum. 
The  green  contains  a  faint  band  in  the  yellow  but  it  is  free  from 
blue.  The  blue  glass  transmits  a  band  in  the  red,  as  is  usually  the 
case  with  blue  glasses,  and  also  faint  lines  in  the  green. 

While,  according  to  our  information,  these  are  the  best  glasses 
that  can  be  obtained,  it  is  readily  seen  that  they  were  unsuitable 
without  some  modifications. 

A  detailed  study  of  monochromatism  of  various  kinds  of  glass 
was  then  undertaken.  A  quantity  of  different  kinds  of  colored 
glass  was  obtained  and  these  glasses  were  all  examined  separately 
by  means  of  a  spectroscope,  and  then  different  combinations  were 
tried  until  the  best  arrangement  was  obtained.  The  Jena  glasses 
were  found  to  be  superior  to  any  examined  but  a  combination  of 
three  different  glasses  was  found  to  give  the  best  results. 

For  example,  some  green  glass  transmits  blue  light  but  no  red, 
while  nearly  all  blue  glass  transmits  some  red;  consequently  a 
combination  of  the  two  is  practically  free  from  red  without  any 
perceptible  reduction  of  the  blue  light. 

In  this  manner  it  was  possible  to  obtain  combinations  for  red, 
green,  and  blue  light  all  of  which  are  practically  monochromatic. 
The  search  for  monochromatic  yellow  was,  however,  futile.  It 
seems  almost  impossible  to  obtain  a  glass  or  a  combination  of 
glasses  which  produces  yellow  and  excludes  all  the  other  colors  in 
even  a  moderate  degree. 

The  fact  that  a  glass  for  a  particular  color  may  contain  a  faint 
band  of  another  color  is  often  of  no  consequence,  providing  that 
consistent  readings  may  be  made,  and  a  very  narrow  band  is  not 
always  necessary  if  the  band  contains  only  one  color.  For  instance, 
we  may  have  a  rather  wide  red  band,  but  so  long  as  there  is  no 
orange  included  in  the  band  a  good  photometric  balance  can  always 
be  made,  and  the  wave-length  used  would  always  be  the  central 
part  of  the  band.  The  difference  between  this  wave-length  and 
the  true  optical  center  of  gravity  is  too  insignificant  to  consider  in 
this  particular  problem. 

There  are  other  methods  for  producing  monochromatic  light, 
but  none  is  very  well  suited  to  this  particular  problem.  The  spec- 


THE  SUN'S  TEMPERATURE  285 

troscopic  eyepiece  designed  by  Mendenhall1  for  pyrometers  using 
the  disappearing-filament  principle  is  best  adapted  to  this  particular 
apparatus,  but  it  was  rejected  for  several  reasons.  In  Menden- 
hall's  pyrometer  a  short  horizontal  section  of  the  lamp-filament 
and  the  superimposed  image  are  focused  upon  the  slit  of  an  auxil- 
iary direct-vision  spectroscope.  The  slit  of  the  spectroscope  is 
vertical  so  that  the  field  is  crossed  by  three  spectra,  the  middle 
one  corresponding  to  the  lamp-filament.  A  diaphragm  is  so  placed 
in  the  focal  plane  of  the  eyepiece  of  the  spectroscope  that  only  the 
desired  region  of  the  spectrum  is  transmitted  to  the  eye.  In  order 
that  this  central  band  may  be  wide  enough  to  make  a  photometric 
comparison  it  is  necessary  to  use  a  very  thick  lamp-filament,  and 
this  is  impossible  when  a  large  magnification  of  the  image  is  required 
as  in  the  present  investigation,  for  then  all  parts  of  the  filament 
would  not  be  in  focus.  Even  with  a  fine  filament  there  is  some 
distortion  of  the  image. 

Furthermore,  any  such  spectroscopic  method  diminishes  the 
intensity  of  the  light  considerably,  making  it  necessary  in  the  blue 
and  violet  region  to  open  both  slits  of  the  instrument  very  wide  in 
order  to  get  sufficient  light  to  make  a  balance.  If  this  is  done,  we 
have  no  longer  strictly  monochromatic  light,  and  we  may  as  well 
employ  colored  glasses.  With  a  colored  glass  one  sees  the  filament 
and  sun's  image  directly  so  that  he  always  knows  just  what  part 
of  the  disk  he  is  on,  but  with  the  spectroscopic  eyepiece  this  of 
course  is  not  the  case,  and  he  must  depend  entirely  upon  the 
finder. 

It  has  been  shown  by  a  number  of  experimenters  that  the 
disappearing-filament  principle  is  by  far  the  most  sensitive  photo- 
metric scheme  that  we  have,  and  it  is  particularly  adapted  to  this 
problem,  since  one  can  move  the  filament  about  to  any  point  on 
the  sun's  image,  and  make  a  temperature  measurement  at  that 
point. 

The  wave-lengths  of  the  monochromatic  glasses  were  deter- 
mined by  means  of  a  Lummer-Brodhun  spectrophotometer"  made 
by  Schmidt  and  Hensch.  The  same  instrument  was  also  used  to 
determine  the  absorption  coefficients  of  the  absorption  glasses. 

1  Physical  Review,  33,  i,  1911. 


286 


GLENN  A.  SHOOK 


DATA  AND  RESULTS 

i.  Wave-lengths  of  the  monochromatic  glasses. — The  readings 
of  the  arbitrary  scale  of  the  Lummer-Brodhun  spectrophotometer 
for  the  three  colored  glasses  used  are  given  in  the  following  tables: 

TABLE  II 
OCULAR  SLIT  =  0.05  CM        SLIT  No.  i,  50 


RED 

GLASS 

GREEN 

GLASS 

BLUE 

GLASS 

Blue  End 

Red  End 

Blue  End 

Red  End 

Blue  End 

Red  End 

616 

546 

734 

654 

994 

750 

618 

546 

732 

654 

994 

748 

614 

544 

734 

652 

990 

750 

618 

546 

736 

654 

994 

748 

616 

542 

736 

652 

994 

752 

616 

546 

734 

656 

1,000 

750 

616 

544 

734 

656 

1,002 

748 

616 

546 

736 

654 

996 

75° 

614 

546 

736 

654 

994 

748 

614 

544 

734 

654 

996 

754 

Mean 

q8o 

Mean 

604. 

Mean 

868 

The  blue  light  was  very  faint,  hence  the  readings  are  not  quite 
so  consistent  as  in  the  case  of  the  red  and  green. 

The  wave-lengths  in  ju,  corresponding  to  these  arbitrary  scale 
readings,  are  as  follows: 


TABLE  III 


Lummer-Brodhun 
Scale  Reading 

Wave-Length  in  M 

Red  glass   

S8o 

0.661 

Green  glass  

694 

0.537 

Blue  glass  

868 

0.446 

•  2.  Absorption  factors. — In  determining  the  absorption  factor  R 
for  any  particular  glass  the  zero  reading  of  the  Lummer-Brodhun 
spectrophotometer  was  taken  before  and  after  the  observations 
with  the  glass. 

The  standard  lamps  were  connected  in  parallel  to  the  same  mains 
and  the  voltage  was  controlled  by  a  rheostat. 


THE  SUN'S  TEMPERATURE 


287 


Red  Light 


TABLE  IV 


L.-B.  No.  580 
Ocular  Slit  =  0.05  cm 


Zero  Reading 

Volts 

Glass  No.  i 

Volts 

Slit  No. 

I,  <O  O    . 

Slit  No.  i,  loo  

Slit  No. 

2,  Ci  .0.  . 

IO7  .O 

Slit  No.  2,  8.4  

IO7.O 

C,I  .Q.  . 

8.3.  . 

CO  6.  . 

8.4  

C,O.Q.  • 

IO7  .O 

8.3.  . 

IO7.O 

Ci    o 

8  3 

Ci    o 

84 

Ci    o 

'   8  4 

IO7   O 

CT    A 

8  4 

C2   O 

8  T, 

Ci    7 

IO7   O 

8  ?. 

IO7   O 

Mean     5  1  30 

Mean.          8  3 

Glass  No.  i 

Volts 

Glass  No.  i 

Volts 

8  * 

107  o 

8   3 

IO7   O 

8   c 

8   c 

8  4    . 

8  3 

8  4 

8  4    . 

8  3    . 

8  3 

8  5    . 

82          .... 

'     85.. 

8  3 

8  c    . 

107  o 

8  3    . 

IO7   O 

8  2  

8  c    . 

8  3    . 

8  3.  . 

Mean.  .  .8.39 


Mean  ....8.34 
Mean 30  observations . .  8 . 36 


REDETERMINATION  OF  ZERO  READING  OF  INSTRUMENT 


Volts 

Slit  No. 

I     CQ    O 

107  o 

Slit  No.  2,  52  3 

Slit  No.  2,  51.3 

Slit  No 

2     C2    6 

C2    3 

CI  .  7 

CT    3  . 

C2.  3 

CO.  ^ 

C.2    O     . 

Ci  .  7 

co.  <; 

CT       C  .    . 

<?2.2 

CO.  3 

^22.. 

C3.o 

2 
51.6 

CQ    3  .  .  . 

«J2.  7 

51  -i 

C2    1.  . 

51.8 

50.3 

C2   4.  . 

51  -9 

51.2 

C2    2.  . 

52.3 

50.0 

C7    o 

CI     Q 

Mean  of  30  observations . 
First  reading 


51-36 
5I-30 


Mean 51 .33 


288  GLENN  A.  SHOOK 

Calculation  of  the  absorption  factors  for  red  light,  0.661  ju. 

Let  the  reading  of  slit  No.  i  be  Sl  and  slit  No.  2  be  S2  when  no 
glass  is  interposed  between  lamp  and  slit  No.  2.  Also  let  S[  and 
S2  be  the  corresponding  readings  when  a  glass  is  inserted;  then  the 
absorption  factor  R  is 

C>         C  C/         C1 

•  Oi        02        «->i        Oj 


Glass  No.  i.  >.^I  = 

5° 
Glass  No.  2.  .  .  ...............  #2  =  11. 

Glass  No.  3  ..................  #3  =  11. 

whence 

(red)  . 


The  absorption  factors  for  the  green  and  blue  glasses,  obtained 
in  the  same  manner,  are  340  and  656  respectively. 

The  lamps  used  for  estimating  the  sun's  temperature  were  cali- 
brated in  a  small  telescope  of  2.68  cm  aperture.  The  distance 
from  the  filament  to  the  aperture  was  59.8  cm.  In  the  observa- 
tory telescope  the  distance  from  filament  to  aperture  was  157.5  cm 
and  the  aperture  was  i  .  49  cm  in  diameter. 

The  ratio  of  the  two  solid  angles  gives  the  reduction  factor  for 
the  telescope.  We  therefore  obtain: 

TT    (2.68)a.7r     (i.49)a  = 
4  "(59.  8)'*  4*  (157.  5)' 

The  resultant  reduction  factors  for  the  three  colors  then  become  : 

Foro.66i/A    #  =  22.3X1725  =  38,500  (i) 

0.537/x    #  =  22.  3X  340  =  7580  (2) 

0.446/4,    #  =  22.  3X  656  =  14,610  (3) 

3.  Temperature  measurement  of  the  sun's  disk.  —  The  distance 
across  the  sun's  disk  was  measured  by  means  of  a  micrometer  scale 
in  the  finder  of  the  telescope,  but  the  number  corresponding  to  the 
center  of  the  disk  would  of  course  change  if  the  lamp  were  raised 
or  lowered.  For  the  observations  carried  out  for  the  red  and  green 
light  54  corresponded  to  the  center  of  the  disk  and  69  to  the  extreme 
edge  or  limb. 


THE  SUN'S  TEMPERATURE 


289 


The  radius  of  the  disk  is  thus  equal  to  15  divisions  on  the  scale 
of  the  finder.  In  the  following  tables  the  readings  of  the  ammeter 
are  given  for  various  distances  from  the  center  of  the  disk.  When 
the  filament  was  adjusted  to  the  desired  point  on  the  disk  the 
current  through  the  filament  was  varied  continuously  until  the  tip 
had  the  same  intrinsic  intensity  as  the  region  surrounding  it  or 
until  it  disappeared  against  the  disk. 

The  following  (Table  V)  is  a  sample  of  the  data  obtained  for  the 
variation  of  the  temperature  with  distance  from  the  edge  to  the 
center  of  the  disk. 

TABLE  V 
AMMETER  READINGS  FOR  GREEN  LIGHT 


69 

68 

67 

64 

80.0 

84.0 

86.0 

91  .0 

82.0 

84.5 

87.5 

Qi-S 

79-5 

83.5 

87.0 

89.5 

81.0 

83.5 

86.5 

89.0 

81.0 

83-5 

88.5 

91  .0 

81.0 

83.0 

87.5 

9i-5 

81.0 

85-0 

87-5 

89-5 

82.0 

82.5 

86.5 

9°-5 

8i.5 

82.5 

87.5 

9i-S 

81.0 

82.5 

85.5 

90.0 

Mean.  .  .  .81.  i 

Mean  83  .  5 

Mean  87.0 

Mean  91.0 

60 

54 

69 

69 

69 

92.0 

93-5 

81.5 

80.0 

80.0 

93-o 

92.5 

82.0 

80.5 

80.0 

9I-5 

93-5 

8i.5 

8i.S 

8i.S 

9i-S 

93-0 

82.0 

80.5 

80.0 

93-o 

91  .0 

8i-5 

80.0 

80.5 

93-0 

92.0 

8i.S 

80.0 

82.0 

92.5 

92.0 

81.0 

82.0 

80.0 

9i-5 

92.0 

82.0 

80.0 

80.5 

92.5 

91-5 

81.5 

81.0 

81.0 

91.0 

9i  5 

81.5 

8i-5 

80.0 

Mean.  92.  2 

Mean.  92.  3 

Mean  of  30  observations  81  .0 

In  this  case  the  observation  on  the  edge,  i.e.,  69,  was  repeated 
and  it  is  seen  that  the  agreement  is  better  than  might  be  expected 
considering  the  uncertainties  of  such  measurements. 


2QO  GLENN  A.  SHOOK 

Instead  of  reducing  these  readings  to  temperatures  of  the  sun's 
disk,  a  curve  was  plotted  for  each  color,  co-ordinating  ammeter 
readings  and  distances  from  center  of  disk.  For  any  particular 
distance,  the  corresponding  ammeter  reading  may  be  obtained 
directly  from  the  curve.  This  gives  a  better  average  of  all  the 
values  taken  across  the  disk. 

4.  Reduction  of  an  observation. — Since  it  is  somewhat  easier  to 
use  Wien's  formula  for  the  reduction  of  these  temperatures,  that 
formula  will  be  used  for  all  the  calculations.  A  temperature  esti- 
mation will  also  be  made  by  means  of  Planck's  formula  to  show  the 
difference  in  the  two  results. 

We  shall  consider  in  detail  only  the  data  obtained  for  red  light, 
as  the  same  method  applies  equally  well  to  green  and  blue. 

Let  Tr  equal  the  black-body  temperature  of  the  sun's  disk,  E' 
the  intensity  of  radiation  incident  upon  the  objective  of  the  tele- 
scope. Also  let  T  be  the  apparent  temperature  of  the  sun's  image 
and  E  the  intensity  of  the  energy  transmitted  by  the  absorbing 
media  of  the  telescope. 

Wien's  formula  may  now  be  written  for  the  two  cases  as  follows: 

log  E'  =  h—k^Y/  (4) 

and 

\ogE=kl-k2^.  (5) 

Subtracting  (5)  from  (4)  we  obtain: 

E'  _ 

But 


where  R  is  the  reduction  factor  of  the  telescope. 

Whence 

^_j^_logff       ^        \ogRX 

T    T       k2  14,500X0.4343 

From  (i): 

7^  =  38,500 
and 

X  =  o.66i . 


THE  SUN'S  TEMPERATURE 


291 


Therefore 


whence 


L    log  38,500X0.661 
k  =  —       >J  —=0.00048: 

14,500X0.4343 


^7  =  ^-0.000482. 


(6) 


Now  consider  curve  i,  Fig.  4,  for  scale  divisions,  54,  i.e.,  the 
center  of  the  sun's  image;  the  ammeter  reading  is  67.2,  and  this 
corresponds  to  a  temperature  of  1317°  C.  or  1590°  A.  If  we  sub- 
stitute this  value  for  T  in  equation  (6)  we  obtain  for  T  the 


68 


66 


64 


62 


60 


69     67 


65 


63          61 
FIG.  4 


59 


57 


55        53 


temperature  of  the  sun's  disk,  a  value  of  6803°  A.  In  this  manner 
data  were  obtained  for  curves  2,  3,  and  4,  Fig.  5. 

As  we  move  from  the  center  of  the  disk  toward  the  limb,  the 
temperature  falls  off  more  rapidly  for  the  shorter  wave-lengths, 
but  near  the  limb  it  falls  off  less  rapidly. 

There  has  always  been  considerable  discussion  as  to  the  best 
value  of  the  constant  C2.  The  value  used  by  Lummer,  Prings- 
heim,  Paschen,  and  Wanner  is  14,500.  Our  own  Bureau  of  Stand- 
ards1 also  accepts  the  same  value  but  the  value  determined  by 


1  Bulletin  Bureau  of  Standards,  3,  No.  2. 


2Q2 


GLENN  A.  SHOOK 


Holborn  and  Valentiner  is  much  lower   14, 200.'     Again,  Nernst 
and  Wartenberg  use  the  value  i4,6oo.2     To  show  the  effect  of  the 


7000*) 


6000 


5000 


4000 


3000 


69       67      65       63 


57 


55 


53 


61         59 
FIG.  5 

variation  of  this  constant  on  the  value  of  the  temperature  of  the 
sun,  the  following  values  were  calculated  for  red  and  blue  light: 

TABLE  VI 


c, 

Red  0.66/A 
T 

Blue  0.446  M 

14,000  

6135 

4310 

14,100  

6211 

4348 

14  2OO 

6320 

4386 

14.  3OO 

6404 

4425 

14,400  

i  A.  <oo 

6667 
6803 

4464 
4505 

14,600  

14,700  

6944 
7143 

4545 
4587 

14,800  

7299 

4630 

1  Ann.  der  Physik,  22,  i,  1907. 

2  Verh.  der  deiitschen  phys.  Ges.,  8,  48,  1906. 


THE  SUN'S  TEMPERATURE  293 

We  will  now  determine  the  value  of  the  temperature  for  red 
light  X  =  o.66i  ju  by  means  of  Planck's  formula  in  order  to  see  what 
error  results  by  using  Wien's  formula. 

Using  the  same  notation,  we  may  write  Planck's  formula  for 
the  two  temperatures  as  follows: 


'•^r  w 

and 

77          /"«    ^  —  c;  I  /0\ 

^   CiA    ~T; • 

Dividing  (8)  by  (7)  we  obtain: 

£/=(^-i)=7g  (9) 

Writing  (9)  in  the  form: 
we  finally  obtain : 

.         r'=^-| =•  M 

Now  let 
whence 


log  e  =  k, 


T' i^-r1    —  •  (») 

log  r^(«Ar-i)-+ 


To  evaluate  ^Ar  let 

^2 


whence 
and 


t  ,.          = 

0.661X1590 


=  977,000 


294 
Since 


GLENN  A.  SHOOK 


R  =  38,500 


The  constant  k2  is  9520  and  the  real  temperature  now  becomes: 


1.420 


If  we  neglect  the  i  in  the  expression  ^(25.3+1),  then  the 
expression  reduces  to  Wien's  formula  in  which  case 


whence 


log  25.3  =  1.403 


1-403 


5300 


5000 


4500 


4000 


The  variation  of  the  apparent  temperature  with  the  sun's 
zenith  distance  was  determined  for  green  light  and  the  results  are 
shown  in  curve  5,  Fig.  6. 


THE  SUN'S  TEMPERATURE  295 

5.  Correction  for  atmospheric  absorption.  —  The  ratio  of  the 
intensity  of  the  sun,  at  the  boundary  of  the  atmosphere  and  at 
the  surface  of  the  earth,  is  given  by  the  well  known  formula: 


where 

Es  =  intensity  of  sun  at  the  boundary  of  the  atmosphere 
Ee  =  intensity  of  sun  at  the  telescope 
A  =the  transmission  coefficient 
Z  =  the  zenith  distance 

If  the  intensity  is  known  for  two  different  hours,  say  12:00 
and  4:00  o'clock,  then  A  may  be  determined  from  the  relation: 


By  means  of  curve  5,  the  apparent  temperature  of  the  sun  for 
these  two  hours  may  be  determined  and  by  means  of  Wien's 
formula  the  ratio  of  the  corresponding  intensities  may  be  deter- 
mined. Writing  Wien's  formula  for  the  two  cases  we  obtain: 

J-  12 

and 


whence 


"*  !-*•(?;-£)•  (I4) 


By  means  of  (14),  using  the  data  obtained  from  curve  5,  we 
obtain: 

log— =0.14 

and  by  means  of  tables 

ZI3  =  i7.i  and  £4  =  54.3 


296  GLENN  A.  SHOOK 

whence 

log  A  — '- =  o .  80^  —  i 

sec  ly.i-sec  54.3 

and 

A  =  o .  63  . 

The  mean  of  5  values  of  A  determined  for  2:00,  3:00,  4:00, 
5:00,  and  6:00  o'clock  was  found  to  be  0.64. 

Using  the  values  of  the  transmission  coefficients  obtained  for 
Washington  and  Mount  Wilson1  the  following  values  were  found 
by  interpolation  for  red  and  blue  light: 

For  red  light,  o.66iju,  ^=0.74,  and  for  blue  light,  0.446/4, 
A  =0.50. 

The  absorption  factor  already  determined  for  the  telescope  will 
now  be  determined  for  red  light,  0.661  ju. 

Equation  (12)  may  be  written  in  the  form 

log  I?  =- sec  Z  log  A  . 

J^e 

The  time  of  observation  of  the  temperature  for  red  light  was 
2:00  P.M.,  September  i,  1912,  and  the  zenith  distance  for  this  hour 
is  42? 7.  We  therefore  obtain: 

Tf 

log— 5=-sec42.7Xlog  0.74  =  0.178 

and 

ft 

^=1.505. 

The  reduction  factor  for  red  light,  0.661  /x,  corrected  for  atmos- 
pheric absorption  now  becomes: 

R'  =  38,5ooX  i .  505  =  58,000 

and  the  new  constant  k'  is 

,,    log  58,000X0.661 
k  =    *  °  '  —=0.000498. 

14,500X0.4343 

1  Abbot,  The  Sun,  p.  242. 


THE  SUN'S  TEMPERATURE  297 

Equation  (6)  therefore  becomes: 

Yf  =  T~~  °-00°498 

and  the  corrected  temperature  for  the  center  of  the  disk  is  7580°  A. 
In  a  similar  manner  the  reduction  factors  for  the  other  colors  were 
found  to  be  15,300  for  green  and  37,000  for  blue  light.  The  data 
for  green  light  were  determined  on  September  22,  1912,  at  2:00 
P.M.,  and  that  for  blue  light  on  April  15,  1913,  at  -2  :oo  P.M. 

The  sun's  temperature  for  the  three  colors  is  therefore  as 

follows : 

For  red  light,  0.661  ^17580°  A. 

For  green  light,  o.  537  /x:  5990°  A. 
For  blue  light,  0.446  /x:  5230°  A. 

Without  the  absorption  of  the  light  through  the  atmosphere  of 
the  earth  we  find  for  the  three  colors  the  following  values: 

For  red  light  6803°  A. 
For  green  light  5208°  A. 
For  blue  light  4505°  A. 

There  is  possibly  a  small  error  in  the  determination  of  the  trans- 
mission coefficients  of  the  atmosphere,  due  to  the  fact  that  these 
coefficients  were  not  determined  at  the  same  time  and  therefore 
possibly  not  under  exactly  the  same  conditions  of  the  atmosphere 
as  those  \:nder  which  the  radiation  of  the  sun  was  measured. 

The  last  two  series  of  values  indicate  clearly  that  the  sun  is  not 
a  black  body,  because  for  a  black  body  we  should  find  the  same 
temperature  for  each  wave-length.  This  fact  is  also  demonstrated 
directly  by  the  actual  distribution  of  the  energy  of  radiation  through 
the  spectrum  and  through  the  results  of  the  three  general  methods 
which  may  be  used  for  the  determination  of  the  sun's  temperature 
based  upon  the  following  laws: 

Stefan-Boltzman  Radiation  Law: 


Wien's  Displacement  Law: 


298  GLENN  A.  SHOOK 

Planck's  Distribution  Law: 


The  first  method  gives  a  temperature  of  5830°  A.  if  we  use 
Abbot's  value  of  the  solar  constant  1.922.  In  the  second  method, 
if  we  take  the  wave-length  of  the  maximum  energy  as  0.470  ju1  we 
get  a  temperature  of  6230°  A.  The  third  method,  as  has  just  been 
shown  by  the  present  investigation,  gives  a  temperature  of  7580°  A. 
All  the  determinations  of  the  temperature  of  the  sun  by  means  of 
radiation  give  therefore  only  approximative  results,  and  the  devia- 
tions of  the  temperatures  for  different  colors  and  for  different 
methods  indicate  how  far  the  sun's  radiation  differs  from  that  of  a 
black  body.  Another  example  taken  from  laboratory  practice 
may  illustrate  the  difference  between  the  thermodynamic  tem- 
perature of  a  radiating  body  and  the  temperature  obtained  by 
radiation  methods.  If  we  attempt  to  measure  the  temperature 
of  a  piece  of  iron  at  about  1600°  A.,  by  means  of  the  total  radiation 
emitted  we  obtain  a  temperature  which  is  about  400°  lower  than 
the  true  temperature,  but  if  we  utilize  the  radiation  corresponding 
to  a  single  wave-length,  say  0.6  ju,  we  obtain  a  temperature  which 
is  about  150°  lower. 

SUMMARY 

1.  The  temperature  of  the  sun  has  been  measured  by  a  new 
method  based  on  Planck's  and  Wien's  laws  of  radiation  for  three 
different  wave-lengths. 

2.  The  variation  of  the  radiation  of  the  sun  from  the  center  to 
the  limb  has  been  measured  for  three  different  colors. 

3.  The  absorption  of  green  light  in  the  atmosphere  of  the  earth 
has  been  measured. 

In  conclusion  I  wish  to  thank  Professor  A.  P.  Carman  and 
Professor  J.  Kunz  for  their  many  helpful  suggestions  during  the 
investigation  of  the  above  problem. 

LABORATORY  OF  PHYSICS 
UNIVERSITY  OF  ILLINOIS 
October  1913 

1  Abbot,  The  Sun,  p.  69. 


BIOGRAPHICAL 

Glenn  A.  Shook  was  born  at  Osgood,  Indiana,  July  16,  1882. 
He  received  his  early  education  in  the  public  schools  of  Osgood  and 
also  Cincinnati,  Ohio.  He  prepared  for  the  University  in  Moores 
Hill  College,  Moores  Hill,  Indiana,  1900-1903.  He  attended  Pur- 
due University,  1903-1906,  and  University  of  Wisconsin,  1906-1907, 
where  he  received  the  A.B.  degree  in  1907.  He  was  instructor  in 
physics  at  Purdue  University,  1907-1911  and  at  University  of  Illi- 
nois, 1911-1914.  His  graduate  work  was  done  during  a  period  of 
four  years  at  Purdue  University  and  of  three  years  at  University 
of  Illinois. 

In  addition  to  some  minor  papers  he  published  the  following 
articles : 

"A  Proposed  Method  of  Calibration  of  Optical  Pyrometers," 
Phys.  Rev.  1910. 

Five  articles  on  "  Radiation  Pyrometry,"  Met.  and  Chem.  Eng., 
1912. 

"  Rechnungsapparat  fur  die  Bestimmung  von  Thermodyna- 
mischen  Tempera turen,"  Physik.  Zeit.,  1912. 

Three  articles  on  "  Quantitative  Spectrum  Analysis,  Met.  and 
Chem.  Eng.j  1913. 


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